Glencoe Algebra 2 Student Edition C2014
1st Edition
ISBN: 9780076639908
Author: McGraw-Hill Glencoe
Publisher: MCG
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Question
Chapter 4.3, Problem 4DGP
To determine
To calculate: The factors of the polynomial −12x2+8x+15 .
Expert Solution & Answer
Answer to Problem 4DGP
The factors of the polynomial −12x2+8x+15 are −6x−5 and 2x−3 .
Explanation of Solution
Given information:
The expression −12x2+8x+15 .
Formula used:
To find the factor of the trinomial of the form ax2+bx+c , find the numbers p,q,r and s such that sum of product of two numbers is equal to coefficient of x(ps+qr=b) , product of p and q is equal to the coefficient of x2pq=a and product of r and s numbers is equal to constant term (r⋅s=c) , such that (px+r) and (qx+s) are the factors of ax2+bx+c .
ax2+bx+c=pqx2+(ps+qr)x+rs=pqx2+psx+qrx+rs=px(qx+s)+r(qx+s)=(px+r)(qx+s)
Calculation:
Consider the given expression −12x2+8x+15 .
Recall that to find the factor of the trinomial of the form ax2+bx+c , find the numbers p,q,r and s such that sum of product of two numbers is equal to coefficient of x(ps+qr=b) , product of p and q is equal to the coefficient of x2(pq=a) and product of r and s numbers is equal to constant term (r⋅s=c) , such that (px+r) and (qx+s) are the factors of ax2+bx+c .
ax2+bx+c=pqx2+(ps+qr)x+rs=pqx2+psx+qrx+rs=px(qx+s)+r(qx+s)=(px+r)(qx+s)
So, find p,q,r and s such that pq=−12 , ps+qr=8 and rs=15 .
So, −12x2+8x+15 will be factorized as,
−12x2+8x+15=−12x2+18x−10x+15=−6x(2x−3)−5(2x−3)=(−6x−5)(2x−3)
Thus, the factors of polynomial −12x2+8x+15 are −6x−5 and 2x−3 .
Chapter 4 Solutions
Glencoe Algebra 2 Student Edition C2014
Ch. 4.1 - Prob. 1AGPCh. 4.1 - Prob. 1BGPCh. 4.1 - Prob. 2GPCh. 4.1 - Prob. 3GPCh. 4.1 - Prob. 4GPCh. 4.1 - Prob. 1CYUCh. 4.1 - Prob. 2CYUCh. 4.1 - Prob. 3CYUCh. 4.1 - Prob. 4CYUCh. 4.1 - Prob. 5CYU
Ch. 4.1 - Prob. 6CYUCh. 4.1 - Prob. 7CYUCh. 4.1 - Prob. 8CYUCh. 4.1 - Prob. 9CYUCh. 4.1 - Prob. 10CYUCh. 4.1 - Prob. 11CYUCh. 4.1 - Prob. 12PPSCh. 4.1 - Prob. 13PPSCh. 4.1 - Prob. 14PPSCh. 4.1 - Prob. 15PPSCh. 4.1 - Prob. 16PPSCh. 4.1 - Prob. 17PPSCh. 4.1 - Prob. 18PPSCh. 4.1 - Prob. 19PPSCh. 4.1 - Prob. 20PPSCh. 4.1 - Prob. 21PPSCh. 4.1 - Prob. 22PPSCh. 4.1 - Prob. 23PPSCh. 4.1 - Prob. 24PPSCh. 4.1 - Prob. 25PPSCh. 4.1 - Prob. 26PPSCh. 4.1 - Prob. 27PPSCh. 4.1 - Prob. 28PPSCh. 4.1 - Prob. 29PPSCh. 4.1 - Prob. 30PPSCh. 4.1 - Prob. 31PPSCh. 4.1 - Prob. 32PPSCh. 4.1 - Prob. 33PPSCh. 4.1 - Prob. 34PPSCh. 4.1 - Prob. 35PPSCh. 4.1 - Prob. 36PPSCh. 4.1 - Prob. 37PPSCh. 4.1 - Prob. 38PPSCh. 4.1 - Prob. 39PPSCh. 4.1 - Prob. 40PPSCh. 4.1 - Prob. 41PPSCh. 4.1 - Prob. 42PPSCh. 4.1 - Prob. 43PPSCh. 4.1 - Prob. 44PPSCh. 4.1 - Prob. 45PPSCh. 4.1 - Prob. 46PPSCh. 4.1 - Prob. 47PPSCh. 4.1 - Prob. 48PPSCh. 4.1 - Prob. 49PPSCh. 4.1 - Prob. 50PPSCh. 4.1 - Prob. 51PPSCh. 4.1 - Prob. 52PPSCh. 4.1 - Prob. 53PPSCh. 4.1 - Prob. 54PPSCh. 4.1 - Prob. 55PPSCh. 4.1 - Prob. 56PPSCh. 4.1 - Prob. 57PPSCh. 4.1 - Prob. 58PPSCh. 4.1 - Prob. 59PPSCh. 4.1 - Prob. 60PPSCh. 4.1 - Prob. 61HPCh. 4.1 - Prob. 62HPCh. 4.1 - Prob. 63HPCh. 4.1 - Prob. 64HPCh. 4.1 - Prob. 65HPCh. 4.1 - Prob. 66STPCh. 4.1 - Prob. 67STPCh. 4.1 - Prob. 68STPCh. 4.1 - Prob. 69STPCh. 4.1 - Prob. 70SRCh. 4.1 - Prob. 71SRCh. 4.1 - Prob. 72SRCh. 4.1 - Prob. 73SRCh. 4.1 - Prob. 74SRCh. 4.1 - Prob. 75SRCh. 4.1 - Prob. 76SRCh. 4.1 - Prob. 77SRCh. 4.1 - Prob. 78SRCh. 4.1 - Prob. 79SRCh. 4.1 - Prob. 80SCh. 4.1 - Prob. 81SCh. 4.1 - Prob. 82SCh. 4.1 - Prob. 1ECh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.2 - Prob. 1AGPCh. 4.2 - Prob. 1BGPCh. 4.2 - Prob. 2AGPCh. 4.2 - Prob. 2BGPCh. 4.2 - Prob. 3GPCh. 4.2 - Prob. 4GPCh. 4.2 - Prob. 5GPCh. 4.2 - Prob. 6GPCh. 4.2 - Prob. 1CYUCh. 4.2 - Prob. 2CYUCh. 4.2 - Prob. 3CYUCh. 4.2 - Prob. 4CYUCh. 4.2 - Prob. 5CYUCh. 4.2 - Prob. 6CYUCh. 4.2 - Prob. 7CYUCh. 4.2 - Prob. 8CYUCh. 4.2 - Prob. 9CYUCh. 4.2 - Prob. 10CYUCh. 4.2 - Prob. 11CYUCh. 4.2 - Prob. 12CYUCh. 4.2 - Prob. 13CYUCh. 4.2 - Prob. 14PPSCh. 4.2 - Prob. 15PPSCh. 4.2 - Prob. 16PPSCh. 4.2 - Prob. 17PPSCh. 4.2 - Prob. 18PPSCh. 4.2 - Prob. 19PPSCh. 4.2 - Prob. 20PPSCh. 4.2 - Prob. 21PPSCh. 4.2 - Prob. 22PPSCh. 4.2 - Prob. 23PPSCh. 4.2 - Prob. 24PPSCh. 4.2 - Prob. 25PPSCh. 4.2 - Prob. 26PPSCh. 4.2 - Prob. 27PPSCh. 4.2 - Prob. 28PPSCh. 4.2 - Prob. 29PPSCh. 4.2 - Prob. 30PPSCh. 4.2 - Prob. 31PPSCh. 4.2 - Prob. 32PPSCh. 4.2 - Prob. 33PPSCh. 4.2 - Prob. 34PPSCh. 4.2 - Prob. 35PPSCh. 4.2 - Prob. 36PPSCh. 4.2 - Prob. 37PPSCh. 4.2 - Prob. 38PPSCh. 4.2 - Prob. 39PPSCh. 4.2 - Prob. 40PPSCh. 4.2 - Prob. 41PPSCh. 4.2 - Prob. 42PPSCh. 4.2 - Prob. 43PPSCh. 4.2 - Prob. 44PPSCh. 4.2 - Prob. 45PPSCh. 4.2 - Prob. 46PPSCh. 4.2 - Prob. 47PPSCh. 4.2 - Prob. 48PPSCh. 4.2 - Prob. 49PPSCh. 4.2 - Prob. 50PPSCh. 4.2 - Prob. 51PPSCh. 4.2 - Prob. 52HPCh. 4.2 - Prob. 53HPCh. 4.2 - Prob. 54HPCh. 4.2 - Prob. 55HPCh. 4.2 - Prob. 56HPCh. 4.2 - Prob. 57STPCh. 4.2 - Prob. 58STPCh. 4.2 - Prob. 59STPCh. 4.2 - Prob. 60STPCh. 4.2 - Prob. 61SRCh. 4.2 - Prob. 62SRCh. 4.2 - Prob. 63SRCh. 4.2 - Prob. 64SRCh. 4.2 - Prob. 65SRCh. 4.2 - Prob. 66SRCh. 4.2 - Prob. 67SRCh. 4.2 - Prob. 68SRCh. 4.2 - Prob. 69SRCh. 4.2 - Prob. 70SRCh. 4.2 - Prob. 71SRCh. 4.2 - Prob. 72SRCh. 4.2 - Prob. 73SRCh. 4.2 - Prob. 74SCh. 4.2 - Prob. 75SCh. 4.2 - Prob. 76SCh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.3 - Prob. 1GPCh. 4.3 - Prob. 2AGPCh. 4.3 - Prob. 2BGPCh. 4.3 - Prob. 2CGPCh. 4.3 - Prob. 3AGPCh. 4.3 - Prob. 3BGPCh. 4.3 - Prob. 3CGPCh. 4.3 - Prob. 4AGPCh. 4.3 - Prob. 4BGPCh. 4.3 - Prob. 4CGPCh. 4.3 - Prob. 4DGPCh. 4.3 - Prob. 5GPCh. 4.3 - Prob. 1CYUCh. 4.3 - Prob. 2CYUCh. 4.3 - Prob. 3CYUCh. 4.3 - Prob. 4CYUCh. 4.3 - Prob. 5CYUCh. 4.3 - Prob. 6CYUCh. 4.3 - Prob. 7CYUCh. 4.3 - Prob. 8CYUCh. 4.3 - Prob. 9CYUCh. 4.3 - Prob. 10CYUCh. 4.3 - Prob. 11CYUCh. 4.3 - Prob. 12CYUCh. 4.3 - Prob. 13CYUCh. 4.3 - Prob. 14CYUCh. 4.3 - Prob. 15CYUCh. 4.3 - Prob. 16CYUCh. 4.3 - Prob. 17PPSCh. 4.3 - Prob. 18PPSCh. 4.3 - Prob. 19PPSCh. 4.3 - Prob. 20PPSCh. 4.3 - Prob. 21PPSCh. 4.3 - Prob. 22PPSCh. 4.3 - Prob. 23PPSCh. 4.3 - Prob. 24PPSCh. 4.3 - Prob. 25PPSCh. 4.3 - Prob. 26PPSCh. 4.3 - Prob. 27PPSCh. 4.3 - Prob. 28PPSCh. 4.3 - Prob. 29PPSCh. 4.3 - Prob. 30PPSCh. 4.3 - Prob. 31PPSCh. 4.3 - Prob. 32PPSCh. 4.3 - Prob. 33PPSCh. 4.3 - Prob. 34PPSCh. 4.3 - Prob. 35PPSCh. 4.3 - Prob. 36PPSCh. 4.3 - Prob. 37PPSCh. 4.3 - Prob. 38PPSCh. 4.3 - Prob. 39PPSCh. 4.3 - Prob. 40PPSCh. 4.3 - Prob. 41PPSCh. 4.3 - Prob. 42PPSCh. 4.3 - Prob. 43PPSCh. 4.3 - Prob. 44PPSCh. 4.3 - Prob. 45PPSCh. 4.3 - Prob. 46PPSCh. 4.3 - Prob. 47PPSCh. 4.3 - Prob. 48PPSCh. 4.3 - Prob. 49PPSCh. 4.3 - Prob. 50PPSCh. 4.3 - Prob. 51PPSCh. 4.3 - Prob. 52PPSCh. 4.3 - Prob. 53PPSCh. 4.3 - Prob. 54PPSCh. 4.3 - Prob. 55PPSCh. 4.3 - Prob. 56PPSCh. 4.3 - Prob. 57PPSCh. 4.3 - Prob. 58PPSCh. 4.3 - Prob. 59PPSCh. 4.3 - Prob. 60PPSCh. 4.3 - Prob. 61PPSCh. 4.3 - Prob. 62PPSCh. 4.3 - Prob. 63PPSCh. 4.3 - Prob. 64PPSCh. 4.3 - Prob. 65PPSCh. 4.3 - Prob. 66PPSCh. 4.3 - Prob. 67PPSCh. 4.3 - Prob. 68PPSCh. 4.3 - Prob. 69PPSCh. 4.3 - Prob. 70PPSCh. 4.3 - Prob. 71PPSCh. 4.3 - Prob. 72PPSCh. 4.3 - Prob. 73PPSCh. 4.3 - Prob. 74PPSCh. 4.3 - Prob. 75PPSCh. 4.3 - Prob. 76PPSCh. 4.3 - Prob. 77PPSCh. 4.3 - Prob. 78PPSCh. 4.3 - Prob. 79HPCh. 4.3 - Prob. 80HPCh. 4.3 - Prob. 81HPCh. 4.3 - Prob. 82HPCh. 4.3 - Prob. 83HPCh. 4.3 - Prob. 84HPCh. 4.3 - Prob. 85HPCh. 4.3 - Prob. 86HPCh. 4.3 - Prob. 87STPCh. 4.3 - Prob. 88STPCh. 4.3 - Prob. 89STPCh. 4.3 - Prob. 90STPCh. 4.3 - Prob. 91SRCh. 4.3 - Prob. 92SRCh. 4.3 - Prob. 93SRCh. 4.3 - Prob. 94SRCh. 4.3 - Prob. 95SRCh. 4.3 - Prob. 96SRCh. 4.3 - Prob. 97SRCh. 4.3 - Prob. 98SCh. 4.3 - Prob. 99SCh. 4.3 - Prob. 100SCh. 4.4 - Prob. 1AGPCh. 4.4 - Prob. 1BGPCh. 4.4 - Prob. 2AGPCh. 4.4 - Prob. 2BGPCh. 4.4 - Prob. 2CGPCh. 4.4 - Prob. 3AGPCh. 4.4 - Prob. 3BGPCh. 4.4 - Prob. 4GPCh. 4.4 - Prob. 5AGPCh. 4.4 - Prob. 5BGPCh. 4.4 - Prob. 6GPCh. 4.4 - Prob. 7AGPCh. 4.4 - Prob. 7BGPCh. 4.4 - Prob. 1CYUCh. 4.4 - Prob. 2CYUCh. 4.4 - Prob. 3CYUCh. 4.4 - Prob. 4CYUCh. 4.4 - Prob. 5CYUCh. 4.4 - Prob. 6CYUCh. 4.4 - Prob. 7CYUCh. 4.4 - Prob. 8CYUCh. 4.4 - Prob. 9CYUCh. 4.4 - Prob. 10CYUCh. 4.4 - Prob. 11CYUCh. 4.4 - Prob. 12CYUCh. 4.4 - Prob. 13CYUCh. 4.4 - Prob. 14CYUCh. 4.4 - Prob. 15CYUCh. 4.4 - Prob. 16CYUCh. 4.4 - Prob. 17CYUCh. 4.4 - Prob. 18PPSCh. 4.4 - Prob. 19PPSCh. 4.4 - Prob. 20PPSCh. 4.4 - Prob. 21PPSCh. 4.4 - Prob. 22PPSCh. 4.4 - Prob. 23PPSCh. 4.4 - Prob. 24PPSCh. 4.4 - Prob. 25PPSCh. 4.4 - Prob. 26PPSCh. 4.4 - Prob. 27PPSCh. 4.4 - Prob. 28PPSCh. 4.4 - Prob. 29PPSCh. 4.4 - Prob. 30PPSCh. 4.4 - Prob. 31PPSCh. 4.4 - Prob. 32PPSCh. 4.4 - Prob. 33PPSCh. 4.4 - Prob. 34PPSCh. 4.4 - Prob. 35PPSCh. 4.4 - Prob. 36PPSCh. 4.4 - Prob. 37PPSCh. 4.4 - Prob. 38PPSCh. 4.4 - Prob. 39PPSCh. 4.4 - Prob. 40PPSCh. 4.4 - Prob. 41PPSCh. 4.4 - Prob. 42PPSCh. 4.4 - Prob. 43PPSCh. 4.4 - Prob. 44PPSCh. 4.4 - Prob. 45PPSCh. 4.4 - Prob. 46PPSCh. 4.4 - Prob. 47PPSCh. 4.4 - Prob. 48PPSCh. 4.4 - Prob. 49PPSCh. 4.4 - Prob. 50PPSCh. 4.4 - Prob. 51PPSCh. 4.4 - Prob. 52PPSCh. 4.4 - Prob. 53PPSCh. 4.4 - Prob. 54PPSCh. 4.4 - Prob. 55PPSCh. 4.4 - Prob. 56PPSCh. 4.4 - Prob. 57PPSCh. 4.4 - Prob. 58PPSCh. 4.4 - Prob. 59PPSCh. 4.4 - Prob. 60PPSCh. 4.4 - Prob. 61PPSCh. 4.4 - Prob. 62PPSCh. 4.4 - Prob. 63PPSCh. 4.4 - Prob. 64PPSCh. 4.4 - Prob. 65PPSCh. 4.4 - Prob. 66PPSCh. 4.4 - Prob. 67HPCh. 4.4 - Prob. 68HPCh. 4.4 - Prob. 69HPCh. 4.4 - Prob. 70HPCh. 4.4 - Prob. 71STPCh. 4.4 - Prob. 72STPCh. 4.4 - Prob. 73STPCh. 4.4 - Prob. 74STPCh. 4.4 - Prob. 75SRCh. 4.4 - Prob. 76SRCh. 4.4 - Prob. 77SRCh. 4.4 - Prob. 78SRCh. 4.4 - Prob. 79SRCh. 4.4 - Prob. 80SRCh. 4.4 - Prob. 81SRCh. 4.4 - Prob. 82SRCh. 4.4 - Prob. 83SRCh. 4.4 - Prob. 84SCh. 4.4 - Prob. 85SCh. 4.4 - Prob. 86SCh. 4.4 - Prob. 87SCh. 4.4 - Prob. 88SCh. 4.4 - Prob. 89SCh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.4 - Prob. 1MCQCh. 4.4 - Prob. 2MCQCh. 4.4 - Prob. 3MCQCh. 4.4 - Prob. 4MCQCh. 4.4 - Prob. 5MCQCh. 4.4 - Prob. 6MCQCh. 4.4 - Prob. 7MCQCh. 4.4 - Prob. 8MCQCh. 4.4 - Prob. 9MCQCh. 4.4 - Prob. 10MCQCh. 4.4 - Prob. 11MCQCh. 4.4 - Prob. 12MCQCh. 4.4 - Prob. 13MCQCh. 4.4 - Prob. 14MCQCh. 4.4 - Prob. 15MCQCh. 4.4 - Prob. 16MCQCh. 4.4 - Prob. 17MCQCh. 4.4 - Prob. 18MCQCh. 4.4 - Prob. 19MCQCh. 4.4 - Prob. 20MCQCh. 4.4 - Prob. 21MCQCh. 4.4 - Prob. 22MCQCh. 4.4 - Prob. 23MCQCh. 4.5 - Prob. 1AGPCh. 4.5 - Prob. 1BGPCh. 4.5 - Prob. 2AGPCh. 4.5 - Prob. 2BGPCh. 4.5 - Prob. 3GPCh. 4.5 - Prob. 4AGPCh. 4.5 - Prob. 4BGPCh. 4.5 - Prob. 5AGPCh. 4.5 - Prob. 5BGPCh. 4.5 - Prob. 6AGPCh. 4.5 - Prob. 6BGPCh. 4.5 - Prob. 1CYUCh. 4.5 - Prob. 2CYUCh. 4.5 - Prob. 3CYUCh. 4.5 - Prob. 4CYUCh. 4.5 - Prob. 5CYUCh. 4.5 - Prob. 6CYUCh. 4.5 - Prob. 7CYUCh. 4.5 - Prob. 8CYUCh. 4.5 - Prob. 9CYUCh. 4.5 - Prob. 10CYUCh. 4.5 - Prob. 11CYUCh. 4.5 - Prob. 12CYUCh. 4.5 - Prob. 13CYUCh. 4.5 - Prob. 14PPSCh. 4.5 - Prob. 15PPSCh. 4.5 - Prob. 16PPSCh. 4.5 - Prob. 17PPSCh. 4.5 - Prob. 18PPSCh. 4.5 - Prob. 19PPSCh. 4.5 - Prob. 20PPSCh. 4.5 - Prob. 21PPSCh. 4.5 - Prob. 22PPSCh. 4.5 - Prob. 23PPSCh. 4.5 - Prob. 24PPSCh. 4.5 - Prob. 25PPSCh. 4.5 - Prob. 26PPSCh. 4.5 - Prob. 27PPSCh. 4.5 - Prob. 28PPSCh. 4.5 - Prob. 29PPSCh. 4.5 - Prob. 30PPSCh. 4.5 - Prob. 31PPSCh. 4.5 - Prob. 32PPSCh. 4.5 - Prob. 33PPSCh. 4.5 - Prob. 34PPSCh. 4.5 - Prob. 35PPSCh. 4.5 - Prob. 36PPSCh. 4.5 - Prob. 37PPSCh. 4.5 - Prob. 38PPSCh. 4.5 - Prob. 39PPSCh. 4.5 - Prob. 40PPSCh. 4.5 - Prob. 41PPSCh. 4.5 - Prob. 42PPSCh. 4.5 - Prob. 43PPSCh. 4.5 - Prob. 44PPSCh. 4.5 - Prob. 45PPSCh. 4.5 - Prob. 46PPSCh. 4.5 - Prob. 47PPSCh. 4.5 - Prob. 48PPSCh. 4.5 - Prob. 49PPSCh. 4.5 - Prob. 50PPSCh. 4.5 - Prob. 51PPSCh. 4.5 - Prob. 52PPSCh. 4.5 - Prob. 53PPSCh. 4.5 - Prob. 54PPSCh. 4.5 - Prob. 55PPSCh. 4.5 - Prob. 56PPSCh. 4.5 - Prob. 57PPSCh. 4.5 - Prob. 58HPCh. 4.5 - Prob. 59HPCh. 4.5 - Prob. 60HPCh. 4.5 - Prob. 61HPCh. 4.5 - Prob. 62HPCh. 4.5 - Prob. 63STPCh. 4.5 - Prob. 64STPCh. 4.5 - Prob. 65STPCh. 4.5 - Prob. 66STPCh. 4.5 - Prob. 67SRCh. 4.5 - Prob. 68SRCh. 4.5 - Prob. 69SRCh. 4.5 - Prob. 70SRCh. 4.5 - Prob. 71SRCh. 4.5 - Prob. 72SRCh. 4.5 - Prob. 73SRCh. 4.5 - Prob. 74SRCh. 4.5 - Prob. 75SRCh. 4.5 - Prob. 76SRCh. 4.5 - Prob. 77SRCh. 4.5 - Prob. 78SRCh. 4.5 - Prob. 79SRCh. 4.5 - Prob. 80SRCh. 4.5 - Prob. 81SCh. 4.5 - Prob. 82SCh. 4.5 - Prob. 83SCh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.6 - Prob. 1AGPCh. 4.6 - Prob. 1BGPCh. 4.6 - Prob. 2AGPCh. 4.6 - Prob. 2BGPCh. 4.6 - Prob. 3AGPCh. 4.6 - Prob. 3BGPCh. 4.6 - Prob. 4AGPCh. 4.6 - Prob. 4BGPCh. 4.6 - Prob. 5AGPCh. 4.6 - Prob. 5BGPCh. 4.6 - Prob. 1CYUCh. 4.6 - Prob. 2CYUCh. 4.6 - Prob. 3CYUCh. 4.6 - Prob. 4CYUCh. 4.6 - Prob. 5CYUCh. 4.6 - Prob. 6CYUCh. 4.6 - Prob. 7CYUCh. 4.6 - Prob. 8CYUCh. 4.6 - Prob. 9CYUCh. 4.6 - Prob. 10CYUCh. 4.6 - Prob. 11CYUCh. 4.6 - Prob. 12CYUCh. 4.6 - Prob. 13CYUCh. 4.6 - Prob. 14PPSCh. 4.6 - Prob. 15PPSCh. 4.6 - Prob. 16PPSCh. 4.6 - Prob. 17PPSCh. 4.6 - Prob. 18PPSCh. 4.6 - Prob. 19PPSCh. 4.6 - Prob. 20PPSCh. 4.6 - Prob. 21PPSCh. 4.6 - Prob. 22PPSCh. 4.6 - Prob. 23PPSCh. 4.6 - Prob. 24PPSCh. 4.6 - Prob. 25PPSCh. 4.6 - Prob. 26PPSCh. 4.6 - Prob. 27PPSCh. 4.6 - Prob. 28PPSCh. 4.6 - Prob. 29PPSCh. 4.6 - Prob. 30PPSCh. 4.6 - Prob. 31PPSCh. 4.6 - Prob. 32PPSCh. 4.6 - Prob. 33PPSCh. 4.6 - Prob. 34PPSCh. 4.6 - Prob. 35PPSCh. 4.6 - Prob. 36PPSCh. 4.6 - Prob. 37PPSCh. 4.6 - Prob. 38PPSCh. 4.6 - Prob. 39PPSCh. 4.6 - Prob. 40PPSCh. 4.6 - Prob. 41PPSCh. 4.6 - Prob. 42PPSCh. 4.6 - Prob. 43HPCh. 4.6 - Prob. 44HPCh. 4.6 - Prob. 45HPCh. 4.6 - Prob. 46HPCh. 4.6 - Prob. 47HPCh. 4.6 - Prob. 48HPCh. 4.6 - Prob. 49STPCh. 4.6 - Prob. 50STPCh. 4.6 - Prob. 51STPCh. 4.6 - Prob. 52STPCh. 4.6 - Prob. 53SRCh. 4.6 - Prob. 54SRCh. 4.6 - Prob. 55SRCh. 4.6 - Prob. 56SRCh. 4.6 - Prob. 57SRCh. 4.6 - Prob. 58SRCh. 4.6 - Prob. 59SRCh. 4.6 - Prob. 60SRCh. 4.6 - Prob. 61SCh. 4.6 - Prob. 62SCh. 4.6 - Prob. 63SCh. 4.7 - Prob. 1AGPCh. 4.7 - Prob. 1BGPCh. 4.7 - Prob. 2GPCh. 4.7 - Prob. 3AGPCh. 4.7 - Prob. 3BGPCh. 4.7 - Prob. 1CYUCh. 4.7 - Prob. 2CYUCh. 4.7 - Prob. 3CYUCh. 4.7 - Prob. 4CYUCh. 4.7 - Prob. 5CYUCh. 4.7 - Prob. 6CYUCh. 4.7 - Prob. 7CYUCh. 4.7 - Prob. 8PPSCh. 4.7 - Prob. 9PPSCh. 4.7 - Prob. 10PPSCh. 4.7 - Prob. 11PPSCh. 4.7 - Prob. 12PPSCh. 4.7 - Prob. 13PPSCh. 4.7 - Prob. 14PPSCh. 4.7 - Prob. 15PPSCh. 4.7 - Prob. 16PPSCh. 4.7 - Prob. 17PPSCh. 4.7 - Prob. 18PPSCh. 4.7 - Prob. 19PPSCh. 4.7 - Prob. 20PPSCh. 4.7 - Prob. 21PPSCh. 4.7 - Prob. 22PPSCh. 4.7 - Prob. 23PPSCh. 4.7 - Prob. 24PPSCh. 4.7 - Prob. 25PPSCh. 4.7 - Prob. 26PPSCh. 4.7 - Prob. 27PPSCh. 4.7 - Prob. 28PPSCh. 4.7 - Prob. 29PPSCh. 4.7 - Prob. 30PPSCh. 4.7 - Prob. 31PPSCh. 4.7 - Prob. 32PPSCh. 4.7 - Prob. 33PPSCh. 4.7 - Prob. 34PPSCh. 4.7 - Prob. 35PPSCh. 4.7 - Prob. 36PPSCh. 4.7 - Prob. 37PPSCh. 4.7 - Prob. 38PPSCh. 4.7 - Prob. 39PPSCh. 4.7 - Prob. 40PPSCh. 4.7 - Prob. 41PPSCh. 4.7 - Prob. 42PPSCh. 4.7 - Prob. 43PPSCh. 4.7 - Prob. 44PPSCh. 4.7 - Prob. 45PPSCh. 4.7 - Prob. 46PPSCh. 4.7 - Prob. 47PPSCh. 4.7 - Prob. 48HPCh. 4.7 - Prob. 49HPCh. 4.7 - Prob. 50HPCh. 4.7 - Prob. 51HPCh. 4.7 - Prob. 52HPCh. 4.7 - Prob. 53STPCh. 4.7 - Prob. 54STPCh. 4.7 - Prob. 55STPCh. 4.7 - Prob. 56STPCh. 4.7 - Prob. 57SRCh. 4.7 - Prob. 58SRCh. 4.7 - Prob. 59SRCh. 4.7 - Prob. 60SRCh. 4.7 - Prob. 61SRCh. 4.7 - Prob. 62SRCh. 4.7 - Prob. 63SRCh. 4.7 - Prob. 64SRCh. 4.7 - Prob. 65SRCh. 4.7 - Prob. 66SRCh. 4.7 - Prob. 67SRCh. 4.7 - Prob. 68SRCh. 4.7 - Prob. 69SRCh. 4.7 - Prob. 70SRCh. 4.7 - Prob. 71SRCh. 4.7 - Prob. 72SRCh. 4.7 - Prob. 73SRCh. 4.7 - Prob. 74SCh. 4.7 - Prob. 75SCh. 4.7 - Prob. 76SCh. 4.7 - Prob. 1ECh. 4.7 - Prob. 2ECh. 4.7 - Prob. 3ECh. 4.7 - Prob. 4ECh. 4.8 - Prob. 1AGPCh. 4.8 - Prob. 1BGPCh. 4.8 - Prob. 2AGPCh. 4.8 - Prob. 2BGPCh. 4.8 - Prob. 3AGPCh. 4.8 - Prob. 3BGPCh. 4.8 - Prob. 4GPCh. 4.8 - Prob. 5AGPCh. 4.8 - Prob. 5BGPCh. 4.8 - Prob. 1CYUCh. 4.8 - Prob. 2CYUCh. 4.8 - Prob. 3CYUCh. 4.8 - Prob. 4CYUCh. 4.8 - Prob. 5CYUCh. 4.8 - Prob. 6CYUCh. 4.8 - Prob. 7CYUCh. 4.8 - Prob. 8CYUCh. 4.8 - Prob. 9CYUCh. 4.8 - Prob. 10CYUCh. 4.8 - Prob. 11CYUCh. 4.8 - Prob. 12CYUCh. 4.8 - Prob. 13PPSCh. 4.8 - Prob. 14PPSCh. 4.8 - Prob. 15PPSCh. 4.8 - Prob. 16PPSCh. 4.8 - Prob. 17PPSCh. 4.8 - Prob. 18PPSCh. 4.8 - Prob. 19PPSCh. 4.8 - Prob. 20PPSCh. 4.8 - Prob. 21PPSCh. 4.8 - Prob. 22PPSCh. 4.8 - Prob. 23PPSCh. 4.8 - Prob. 24PPSCh. 4.8 - Prob. 25PPSCh. 4.8 - Prob. 26PPSCh. 4.8 - Prob. 27PPSCh. 4.8 - Prob. 28PPSCh. 4.8 - Prob. 29PPSCh. 4.8 - Prob. 30PPSCh. 4.8 - Prob. 31PPSCh. 4.8 - Prob. 32PPSCh. 4.8 - Prob. 33PPSCh. 4.8 - Prob. 34PPSCh. 4.8 - Prob. 35PPSCh. 4.8 - Prob. 36PPSCh. 4.8 - Prob. 37PPSCh. 4.8 - Prob. 38PPSCh. 4.8 - Prob. 39PPSCh. 4.8 - Prob. 40PPSCh. 4.8 - Prob. 41PPSCh. 4.8 - Prob. 42PPSCh. 4.8 - Prob. 43PPSCh. 4.8 - Prob. 44PPSCh. 4.8 - Prob. 45PPSCh. 4.8 - Prob. 46PPSCh. 4.8 - Prob. 47PPSCh. 4.8 - Prob. 48PPSCh. 4.8 - Prob. 49PPSCh. 4.8 - Prob. 50PPSCh. 4.8 - Prob. 51PPSCh. 4.8 - Prob. 52PPSCh. 4.8 - Prob. 53PPSCh. 4.8 - Prob. 54PPSCh. 4.8 - Prob. 55PPSCh. 4.8 - Prob. 56PPSCh. 4.8 - Prob. 57HPCh. 4.8 - Prob. 58HPCh. 4.8 - Prob. 59HPCh. 4.8 - Prob. 60HPCh. 4.8 - Prob. 61HPCh. 4.8 - Prob. 62HPCh. 4.8 - Prob. 63STPCh. 4.8 - Prob. 64STPCh. 4.8 - Prob. 65STPCh. 4.8 - Prob. 66STPCh. 4.8 - Prob. 67SRCh. 4.8 - Prob. 68SRCh. 4.8 - Prob. 69SRCh. 4.8 - Prob. 70SRCh. 4.8 - Prob. 71SRCh. 4.8 - Prob. 72SRCh. 4.8 - Prob. 73SRCh. 4.8 - Prob. 74SRCh. 4.8 - Prob. 75SRCh. 4.8 - Prob. 76SRCh. 4.8 - Prob. 77SCh. 4.8 - Prob. 78SCh. 4.8 - Prob. 79SCh. 4.8 - Prob. 80SCh. 4.8 - Prob. 81SCh. 4.8 - Prob. 82SCh. 4 - Prob. 1QCCh. 4 - Prob. 2QCCh. 4 - Prob. 3QCCh. 4 - Prob. 4QCCh. 4 - Prob. 5QCCh. 4 - Prob. 6QCCh. 4 - Prob. 7QCCh. 4 - Prob. 8QCCh. 4 - Prob. 9QCCh. 4 - Prob. 10QCCh. 4 - Prob. 11QCCh. 4 - Prob. 12QCCh. 4 - Prob. 13QCCh. 4 - Prob. 14QCCh. 4 - Prob. 15QCCh. 4 - Prob. 1SGRCh. 4 - Prob. 2SGRCh. 4 - Prob. 3SGRCh. 4 - Prob. 4SGRCh. 4 - Prob. 5SGRCh. 4 - Prob. 6SGRCh. 4 - Prob. 7SGRCh. 4 - Prob. 8SGRCh. 4 - Prob. 9SGRCh. 4 - Prob. 10SGRCh. 4 - Prob. 11SGRCh. 4 - Prob. 12SGRCh. 4 - Prob. 13SGRCh. 4 - Prob. 14SGRCh. 4 - Prob. 15SGRCh. 4 - Prob. 16SGRCh. 4 - Prob. 17SGRCh. 4 - Prob. 18SGRCh. 4 - Prob. 19SGRCh. 4 - Prob. 20SGRCh. 4 - Prob. 21SGRCh. 4 - Prob. 22SGRCh. 4 - Prob. 23SGRCh. 4 - Prob. 24SGRCh. 4 - Prob. 25SGRCh. 4 - Prob. 26SGRCh. 4 - Prob. 27SGRCh. 4 - Prob. 28SGRCh. 4 - Prob. 29SGRCh. 4 - Prob. 30SGRCh. 4 - Prob. 31SGRCh. 4 - Prob. 32SGRCh. 4 - Prob. 33SGRCh. 4 - Prob. 34SGRCh. 4 - Prob. 35SGRCh. 4 - Prob. 36SGRCh. 4 - Prob. 37SGRCh. 4 - Prob. 38SGRCh. 4 - Prob. 39SGRCh. 4 - Prob. 40SGRCh. 4 - Prob. 41SGRCh. 4 - Prob. 42SGRCh. 4 - Prob. 43SGRCh. 4 - Prob. 44SGRCh. 4 - Prob. 45SGRCh. 4 - Prob. 46SGRCh. 4 - Prob. 47SGRCh. 4 - Prob. 48SGRCh. 4 - Prob. 49SGRCh. 4 - Prob. 50SGRCh. 4 - Prob. 51SGRCh. 4 - Prob. 52SGRCh. 4 - Prob. 53SGRCh. 4 - Prob. 54SGRCh. 4 - Prob. 55SGRCh. 4 - Prob. 56SGRCh. 4 - Prob. 57SGRCh. 4 - Prob. 58SGRCh. 4 - Prob. 59SGRCh. 4 - Prob. 60SGRCh. 4 - Prob. 61SGRCh. 4 - Prob. 62SGRCh. 4 - Prob. 63SGRCh. 4 - Prob. 64SGRCh. 4 - Prob. 65SGRCh. 4 - Prob. 66SGRCh. 4 - Prob. 67SGRCh. 4 - Prob. 68SGRCh. 4 - Prob. 69SGRCh. 4 - Prob. 70SGRCh. 4 - Prob. 71SGRCh. 4 - Prob. 72SGRCh. 4 - Prob. 73SGRCh. 4 - Prob. 1PTCh. 4 - Prob. 2PTCh. 4 - Prob. 3PTCh. 4 - Prob. 4PTCh. 4 - Prob. 5PTCh. 4 - Prob. 6PTCh. 4 - Prob. 7PTCh. 4 - Prob. 8PTCh. 4 - Prob. 9PTCh. 4 - Prob. 10PTCh. 4 - Prob. 11PTCh. 4 - Prob. 12PTCh. 4 - Prob. 13PTCh. 4 - Prob. 14PTCh. 4 - Prob. 15PTCh. 4 - Prob. 16PTCh. 4 - Prob. 17PTCh. 4 - Prob. 18PTCh. 4 - Prob. 19PTCh. 4 - Prob. 20PTCh. 4 - Prob. 21PTCh. 4 - Prob. 22PTCh. 4 - Prob. 23PTCh. 4 - Prob. 24PTCh. 4 - Prob. 25PTCh. 4 - Prob. 26PTCh. 4 - Prob. 1ECh. 4 - Prob. 2ECh. 4 - Prob. 3ECh. 4 - Prob. 4ECh. 4 - Prob. 5ECh. 4 - Prob. 6ECh. 4 - Prob. 1STPCh. 4 - Prob. 2STPCh. 4 - Prob. 3STPCh. 4 - Prob. 4STPCh. 4 - Prob. 5STPCh. 4 - Prob. 6STPCh. 4 - Prob. 7STPCh. 4 - Prob. 8STPCh. 4 - Prob. 9STPCh. 4 - Prob. 10STPCh. 4 - Prob. 11STPCh. 4 - Prob. 12STPCh. 4 - Prob. 13STPCh. 4 - Prob. 14STPCh. 4 - Prob. 15STPCh. 4 - Prob. 16STP
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