Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Question
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Chapter 5.3, Problem 86HP
To determine

To explain: The factorization of the polynomial of the form ax2+bx+c.

Expert Solution & Answer
Check Mark

Answer to Problem 86HP

The factorization of the polynomial of the form ax2+bx+c is possible by splitting the middle term.

Explanation of Solution

Given information:

The polynomial ax2+bx+c.

Formula used:

To factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

Calculation:

Consider the polynomial of the form ax2+bx+c say 2x2+3x−2

Recall that to factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

For the above polynomial −1 and 4 are two numbers such that their sum is 3 and product is −4.

Apply it, first the group the similar terms,

  2x2+3x−2=2x2−x+4x−2=x(2x−1)+2(2x−1)=(2x−1)(x+2)

Thus, the polynomial is factored as (2x−1)(x+2).

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Chapter 5.3, Problem 85HP
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Chapter 5.3, Problem 87HP

Chapter 5 Solutions

Algebra 2

Ch. 5.1 - Prob. 1ACYPCh. 5.1 - Prob. 1BCYPCh. 5.1 - Prob. 2ACYPCh. 5.1 - Prob. 2BCYPCh. 5.1 - Prob. 2CCYPCh. 5.1 - Prob. 3ACYPCh. 5.1 - Prob. 3BCYPCh. 5.1 - Prob. 3CCYPCh. 5.1 - Prob. 4CYPCh. 5.1 - Prob. 1CYU
Ch. 5.1 - Prob. 2CYUCh. 5.1 - Prob. 3CYUCh. 5.1 - Prob. 4CYUCh. 5.1 - Prob. 5CYUCh. 5.1 - Prob. 6CYUCh. 5.1 - Prob. 7CYUCh. 5.1 - Prob. 8CYUCh. 5.1 - Prob. 9CYUCh. 5.1 - Prob. 10CYUCh. 5.1 - Prob. 11CYUCh. 5.1 - Prob. 12PPSCh. 5.1 - Prob. 13PPSCh. 5.1 - Prob. 14PPSCh. 5.1 - Prob. 15PPSCh. 5.1 - Prob. 16PPSCh. 5.1 - Prob. 17PPSCh. 5.1 - Prob. 18PPSCh. 5.1 - Prob. 19PPSCh. 5.1 - Prob. 20PPSCh. 5.1 - Prob. 21PPSCh. 5.1 - Prob. 22PPSCh. 5.1 - Prob. 23PPSCh. 5.1 - Prob. 24PPSCh. 5.1 - Prob. 25PPSCh. 5.1 - Prob. 26PPSCh. 5.1 - Prob. 27PPSCh. 5.1 - Prob. 28PPSCh. 5.1 - Prob. 29PPSCh. 5.1 - Prob. 30PPSCh. 5.1 - Prob. 31PPSCh. 5.1 - Prob. 32PPSCh. 5.1 - Prob. 33PPSCh. 5.1 - Prob. 34PPSCh. 5.1 - Prob. 35PPSCh. 5.1 - Prob. 36PPSCh. 5.1 - Prob. 37PPSCh. 5.1 - Prob. 38PPSCh. 5.1 - Prob. 39PPSCh. 5.1 - Prob. 40PPSCh. 5.1 - Prob. 41PPSCh. 5.1 - Prob. 42PPSCh. 5.1 - Prob. 43PPSCh. 5.1 - Prob. 44PPSCh. 5.1 - Prob. 45PPSCh. 5.1 - Prob. 46PPSCh. 5.1 - Prob. 47PPSCh. 5.1 - Prob. 48PPSCh. 5.1 - Prob. 49PPSCh. 5.1 - 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Prob. 1BCYPCh. 5.4 - Prob. 2ACYPCh. 5.4 - Prob. 2BCYPCh. 5.4 - Prob. 2CCYPCh. 5.4 - Prob. 3ACYPCh. 5.4 - Prob. 3BCYPCh. 5.4 - Prob. 4CYPCh. 5.4 - Prob. 5ACYPCh. 5.4 - Prob. 5BCYPCh. 5.4 - Prob. 6CYPCh. 5.4 - Prob. 7ACYPCh. 5.4 - Prob. 7BCYPCh. 5.4 - Prob. 1CYUCh. 5.4 - Prob. 2CYUCh. 5.4 - Prob. 3CYUCh. 5.4 - Prob. 4CYUCh. 5.4 - Prob. 5CYUCh. 5.4 - Prob. 6CYUCh. 5.4 - Prob. 7CYUCh. 5.4 - Prob. 8CYUCh. 5.4 - Prob. 9CYUCh. 5.4 - Prob. 10CYUCh. 5.4 - Prob. 11CYUCh. 5.4 - Prob. 12CYUCh. 5.4 - Prob. 13CYUCh. 5.4 - Prob. 14CYUCh. 5.4 - Prob. 15CYUCh. 5.4 - Prob. 16CYUCh. 5.4 - Prob. 17CYUCh. 5.4 - Prob. 18PPSCh. 5.4 - Prob. 19PPSCh. 5.4 - Prob. 20PPSCh. 5.4 - Prob. 21PPSCh. 5.4 - Prob. 22PPSCh. 5.4 - Prob. 23PPSCh. 5.4 - Prob. 24PPSCh. 5.4 - Prob. 25PPSCh. 5.4 - Prob. 26PPSCh. 5.4 - Prob. 27PPSCh. 5.4 - Prob. 28PPSCh. 5.4 - Prob. 29PPSCh. 5.4 - Prob. 30PPSCh. 5.4 - Prob. 31PPSCh. 5.4 - Prob. 32PPSCh. 5.4 - Prob. 33PPSCh. 5.4 - Prob. 34PPSCh. 5.4 - Prob. 35PPSCh. 5.4 - Prob. 36PPSCh. 5.4 - Prob. 37PPSCh. 5.4 - Prob. 38PPSCh. 5.4 - Prob. 39PPSCh. 5.4 - Prob. 40PPSCh. 5.4 - Prob. 41PPSCh. 5.4 - Prob. 42PPSCh. 5.4 - Prob. 43PPSCh. 5.4 - Prob. 44PPSCh. 5.4 - Prob. 45PPSCh. 5.4 - Prob. 46PPSCh. 5.4 - Prob. 47PPSCh. 5.4 - Prob. 48PPSCh. 5.4 - Prob. 49PPSCh. 5.4 - Prob. 50PPSCh. 5.4 - Prob. 51PPSCh. 5.4 - Prob. 52PPSCh. 5.4 - Prob. 53PPSCh. 5.4 - Prob. 54PPSCh. 5.4 - Prob. 55PPSCh. 5.4 - Prob. 56PPSCh. 5.4 - Prob. 57PPSCh. 5.4 - Prob. 58PPSCh. 5.4 - Prob. 59PPSCh. 5.4 - Prob. 60PPSCh. 5.4 - Prob. 61PPSCh. 5.4 - Prob. 62PPSCh. 5.4 - Prob. 63PPSCh. 5.4 - Prob. 64PPSCh. 5.4 - Prob. 65PPSCh. 5.4 - Prob. 66HPCh. 5.4 - Prob. 67HPCh. 5.4 - Prob. 68HPCh. 5.4 - Prob. 69HPCh. 5.4 - Prob. 70HPCh. 5.4 - Prob. 71HPCh. 5.4 - Prob. 72HPCh. 5.4 - Prob. 73HPCh. 5.4 - Prob. 74HPCh. 5.4 - Prob. 75STPCh. 5.4 - Prob. 76STPCh. 5.4 - Prob. 77STPCh. 5.4 - Prob. 78STPCh. 5.4 - Prob. 79STPCh. 5.4 - Prob. 80STPCh. 5.4 - Prob. 81STPCh. 5.4 - Prob. 82STPCh. 5.4 - Prob. 83STPCh. 5.4 - Prob. 84SCh. 5.4 - Prob. 85SCh. 5.4 - Prob. 86SCh. 5.4 - Prob. 87SCh. 5.4 - Prob. 88SCh. 5.4 - Prob. 89SCh. 5.5 - Prob. 1ACYPCh. 5.5 - Prob. 1BCYPCh. 5.5 - Prob. 2ACYPCh. 5.5 - Prob. 2BCYPCh. 5.5 - Prob. 3CYPCh. 5.5 - Prob. 4ACYPCh. 5.5 - Prob. 4BCYPCh. 5.5 - Prob. 5ACYPCh. 5.5 - Prob. 5BCYPCh. 5.5 - Prob. 6ACYPCh. 5.5 - Prob. 6BCYPCh. 5.5 - Prob. 1CYUCh. 5.5 - Prob. 2CYUCh. 5.5 - Prob. 3CYUCh. 5.5 - Prob. 4CYUCh. 5.5 - Prob. 5CYUCh. 5.5 - Prob. 6CYUCh. 5.5 - Prob. 7CYUCh. 5.5 - Prob. 8CYUCh. 5.5 - Prob. 9CYUCh. 5.5 - Prob. 10CYUCh. 5.5 - Prob. 11CYUCh. 5.5 - Prob. 12CYUCh. 5.5 - Prob. 13CYUCh. 5.5 - Prob. 14PPSCh. 5.5 - Prob. 15PPSCh. 5.5 - Prob. 16PPSCh. 5.5 - Prob. 17PPSCh. 5.5 - Prob. 18PPSCh. 5.5 - Prob. 19PPSCh. 5.5 - Prob. 20PPSCh. 5.5 - Prob. 21PPSCh. 5.5 - Prob. 22PPSCh. 5.5 - Prob. 23PPSCh. 5.5 - Prob. 24PPSCh. 5.5 - Prob. 25PPSCh. 5.5 - Prob. 26PPSCh. 5.5 - Prob. 27PPSCh. 5.5 - Prob. 28PPSCh. 5.5 - Prob. 29PPSCh. 5.5 - Prob. 30PPSCh. 5.5 - Prob. 31PPSCh. 5.5 - Prob. 32PPSCh. 5.5 - Prob. 33PPSCh. 5.5 - Prob. 34PPSCh. 5.5 - Prob. 35PPSCh. 5.5 - 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Prob. 5CYUCh. 5.7 - Prob. 6CYUCh. 5.7 - Prob. 7CYUCh. 5.7 - Prob. 8PPSCh. 5.7 - Prob. 9PPSCh. 5.7 - Prob. 10PPSCh. 5.7 - Prob. 11PPSCh. 5.7 - Prob. 12PPSCh. 5.7 - Prob. 13PPSCh. 5.7 - Prob. 14PPSCh. 5.7 - Prob. 15PPSCh. 5.7 - Prob. 16PPSCh. 5.7 - Prob. 17PPSCh. 5.7 - Prob. 18PPSCh. 5.7 - Prob. 19PPSCh. 5.7 - Prob. 20PPSCh. 5.7 - Prob. 21PPSCh. 5.7 - Prob. 22PPSCh. 5.7 - Prob. 23PPSCh. 5.7 - Prob. 24PPSCh. 5.7 - Prob. 25PPSCh. 5.7 - Prob. 26PPSCh. 5.7 - Prob. 27PPSCh. 5.7 - Prob. 28PPSCh. 5.7 - Prob. 29PPSCh. 5.7 - Prob. 30PPSCh. 5.7 - Prob. 31PPSCh. 5.7 - Prob. 32PPSCh. 5.7 - Prob. 33PPSCh. 5.7 - Prob. 34PPSCh. 5.7 - Prob. 35PPSCh. 5.7 - Prob. 36PPSCh. 5.7 - Prob. 37PPSCh. 5.7 - Prob. 38PPSCh. 5.7 - Prob. 39PPSCh. 5.7 - Prob. 40PPSCh. 5.7 - Prob. 41PPSCh. 5.7 - Prob. 42PPSCh. 5.7 - Prob. 43PPSCh. 5.7 - Prob. 44PPSCh. 5.7 - Prob. 45PPSCh. 5.7 - Prob. 46PPSCh. 5.7 - Prob. 47PPSCh. 5.7 - Prob. 48HPCh. 5.7 - Prob. 49HPCh. 5.7 - Prob. 50HPCh. 5.7 - Prob. 51HPCh. 5.7 - Prob. 52HPCh. 5.7 - Prob. 53HPCh. 5.7 - Prob. 54HPCh. 5.7 - Prob. 55HPCh. 5.7 - Prob. 56HPCh. 5.7 - Prob. 57STPCh. 5.7 - Prob. 58STPCh. 5.7 - Prob. 59STPCh. 5.7 - Prob. 60STPCh. 5.7 - Prob. 61STPCh. 5.7 - Prob. 62STPCh. 5.7 - Prob. 63STPCh. 5.7 - Prob. 64STPCh. 5.7 - Prob. 65STPCh. 5.7 - Prob. 66STPCh. 5.7 - Prob. 67STPCh. 5.7 - Prob. 68STPCh. 5.7 - Prob. 69STPCh. 5.7 - Prob. 70STPCh. 5.7 - Prob. 71STPCh. 5.7 - Prob. 72STPCh. 5.7 - Prob. 73STPCh. 5.7 - Prob. 74SCh. 5.7 - Prob. 75SCh. 5.7 - Prob. 76SCh. 5.7 - Prob. 1ECh. 5.7 - Prob. 2ECh. 5.7 - Prob. 3ECh. 5.7 - Prob. 4ECh. 5.8 - Prob. 1ACYPCh. 5.8 - Prob. 1BCYPCh. 5.8 - Prob. 2ACYPCh. 5.8 - Prob. 2BCYPCh. 5.8 - Prob. 3ACYPCh. 5.8 - Prob. 3BCYPCh. 5.8 - Prob. 4CYPCh. 5.8 - Prob. 5ACYPCh. 5.8 - Prob. 5BCYPCh. 5.8 - Prob. 1CYUCh. 5.8 - Prob. 2CYUCh. 5.8 - Prob. 3CYUCh. 5.8 - Prob. 4CYUCh. 5.8 - Prob. 5CYUCh. 5.8 - Prob. 6CYUCh. 5.8 - Prob. 7CYUCh. 5.8 - Prob. 8CYUCh. 5.8 - Prob. 9CYUCh. 5.8 - Prob. 10CYUCh. 5.8 - Prob. 11CYUCh. 5.8 - Prob. 12CYUCh. 5.8 - Prob. 13PPSCh. 5.8 - Prob. 14PPSCh. 5.8 - Prob. 15PPSCh. 5.8 - Prob. 16PPSCh. 5.8 - Prob. 17PPSCh. 5.8 - Prob. 18PPSCh. 5.8 - Prob. 19PPSCh. 5.8 - Prob. 20PPSCh. 5.8 - Prob. 21PPSCh. 5.8 - Prob. 22PPSCh. 5.8 - Prob. 23PPSCh. 5.8 - Prob. 24PPSCh. 5.8 - Prob. 25PPSCh. 5.8 - Prob. 26PPSCh. 5.8 - Prob. 27PPSCh. 5.8 - Prob. 28PPSCh. 5.8 - Prob. 29PPSCh. 5.8 - Prob. 30PPSCh. 5.8 - Prob. 31PPSCh. 5.8 - Prob. 32PPSCh. 5.8 - Prob. 33PPSCh. 5.8 - Prob. 34PPSCh. 5.8 - Prob. 35PPSCh. 5.8 - Prob. 36PPSCh. 5.8 - Prob. 37PPSCh. 5.8 - Prob. 38PPSCh. 5.8 - Prob. 39PPSCh. 5.8 - Prob. 40PPSCh. 5.8 - Prob. 41PPSCh. 5.8 - Prob. 42PPSCh. 5.8 - Prob. 43PPSCh. 5.8 - Prob. 44PPSCh. 5.8 - Prob. 45PPSCh. 5.8 - Prob. 46PPSCh. 5.8 - Prob. 47PPSCh. 5.8 - Prob. 48PPSCh. 5.8 - Prob. 49PPSCh. 5.8 - Prob. 50PPSCh. 5.8 - Prob. 51PPSCh. 5.8 - Prob. 52PPSCh. 5.8 - Prob. 53PPSCh. 5.8 - Prob. 54PPSCh. 5.8 - Prob. 55PPSCh. 5.8 - Prob. 56PPSCh. 5.8 - Prob. 57HPCh. 5.8 - Prob. 58HPCh. 5.8 - Prob. 59HPCh. 5.8 - Prob. 60HPCh. 5.8 - Prob. 61HPCh. 5.8 - Prob. 62HPCh. 5.8 - Prob. 63HPCh. 5.8 - Prob. 64HPCh. 5.8 - Prob. 65HPCh. 5.8 - Prob. 66HPCh. 5.8 - Prob. 67STPCh. 5.8 - Prob. 68STPCh. 5.8 - Prob. 69STPCh. 5.8 - Prob. 70STPCh. 5.8 - Prob. 71STPCh. 5.8 - Prob. 72STPCh. 5.8 - Prob. 73STPCh. 5.8 - Prob. 74STPCh. 5.8 - Prob. 75STPCh. 5.8 - Prob. 76STPCh. 5.8 - Prob. 77SCh. 5.8 - Prob. 78SCh. 5.8 - Prob. 79SCh. 5.8 - Prob. 80SCh. 5.8 - Prob. 81SCh. 5.8 - Prob. 82SCh. 5 - Prob. 1QCCh. 5 - Prob. 2QCCh. 5 - Prob. 3QCCh. 5 - Prob. 4QCCh. 5 - Prob. 5QCCh. 5 - Prob. 6QCCh. 5 - Prob. 7QCCh. 5 - Prob. 8QCCh. 5 - Prob. 9QCCh. 5 - Prob. 10QCCh. 5 - Prob. 11QCCh. 5 - Prob. 12QCCh. 5 - Prob. 13QCCh. 5 - Prob. 14QCCh. 5 - Prob. 15QCCh. 5 - Prob. 1MCQCh. 5 - Prob. 2MCQCh. 5 - Prob. 3MCQCh. 5 - Prob. 4MCQCh. 5 - Prob. 5MCQCh. 5 - Prob. 6MCQCh. 5 - Prob. 7MCQCh. 5 - Prob. 8MCQCh. 5 - Prob. 9MCQCh. 5 - Prob. 10MCQCh. 5 - Prob. 11MCQCh. 5 - Prob. 12MCQCh. 5 - Prob. 13MCQCh. 5 - Prob. 14MCQCh. 5 - Prob. 15MCQCh. 5 - Prob. 16MCQCh. 5 - Prob. 17MCQCh. 5 - Prob. 18MCQCh. 5 - Prob. 19MCQCh. 5 - Prob. 20MCQCh. 5 - Prob. 21MCQCh. 5 - Prob. 22MCQCh. 5 - Prob. 23MCQCh. 5 - Prob. 1SGRCh. 5 - Prob. 2SGRCh. 5 - Prob. 3SGRCh. 5 - Prob. 4SGRCh. 5 - Prob. 5SGRCh. 5 - Prob. 6SGRCh. 5 - Prob. 7SGRCh. 5 - Prob. 8SGRCh. 5 - Prob. 9SGRCh. 5 - Prob. 10SGRCh. 5 - Prob. 11SGRCh. 5 - Prob. 12SGRCh. 5 - Prob. 13SGRCh. 5 - Prob. 14SGRCh. 5 - Prob. 15SGRCh. 5 - Prob. 16SGRCh. 5 - Prob. 17SGRCh. 5 - Prob. 18SGRCh. 5 - Prob. 19SGRCh. 5 - Prob. 20SGRCh. 5 - Prob. 21SGRCh. 5 - Prob. 22SGRCh. 5 - Prob. 23SGRCh. 5 - Prob. 24SGRCh. 5 - Prob. 25SGRCh. 5 - Prob. 26SGRCh. 5 - Prob. 27SGRCh. 5 - Prob. 28SGRCh. 5 - Prob. 29SGRCh. 5 - Prob. 30SGRCh. 5 - Prob. 31SGRCh. 5 - Prob. 32SGRCh. 5 - Prob. 33SGRCh. 5 - Prob. 34SGRCh. 5 - Prob. 35SGRCh. 5 - Prob. 36SGRCh. 5 - Prob. 37SGRCh. 5 - Prob. 38SGRCh. 5 - Prob. 39SGRCh. 5 - Prob. 40SGRCh. 5 - Prob. 41SGRCh. 5 - Prob. 42SGRCh. 5 - Prob. 43SGRCh. 5 - Prob. 44SGRCh. 5 - Prob. 45SGRCh. 5 - Prob. 46SGRCh. 5 - Prob. 47SGRCh. 5 - Prob. 48SGRCh. 5 - Prob. 49SGRCh. 5 - Prob. 50SGRCh. 5 - Prob. 51SGRCh. 5 - Prob. 52SGRCh. 5 - Prob. 53SGRCh. 5 - Prob. 54SGRCh. 5 - Prob. 55SGRCh. 5 - Prob. 56SGRCh. 5 - Prob. 57SGRCh. 5 - Prob. 58SGRCh. 5 - Prob. 59SGRCh. 5 - Prob. 60SGRCh. 5 - Prob. 61SGRCh. 5 - Prob. 62SGRCh. 5 - Prob. 63SGRCh. 5 - Prob. 64SGRCh. 5 - Prob. 65SGRCh. 5 - Prob. 66SGRCh. 5 - Prob. 67SGRCh. 5 - Prob. 68SGRCh. 5 - Prob. 69SGRCh. 5 - Prob. 70SGRCh. 5 - Prob. 71SGRCh. 5 - Prob. 72SGRCh. 5 - Prob. 73SGRCh. 5 - Prob. 1PTCh. 5 - Prob. 2PTCh. 5 - Prob. 3PTCh. 5 - Prob. 4PTCh. 5 - Prob. 5PTCh. 5 - Prob. 6PTCh. 5 - Prob. 7PTCh. 5 - Prob. 8PTCh. 5 - Prob. 9PTCh. 5 - Prob. 10PTCh. 5 - Prob. 11PTCh. 5 - Prob. 12PTCh. 5 - Prob. 13PTCh. 5 - Prob. 14PTCh. 5 - Prob. 15PTCh. 5 - Prob. 16PTCh. 5 - Prob. 17PTCh. 5 - Prob. 18PTCh. 5 - Prob. 19PTCh. 5 - Prob. 20PTCh. 5 - Prob. 21PTCh. 5 - Prob. 22PTCh. 5 - Prob. 23PTCh. 5 - Prob. 24PTCh. 5 - Prob. 25PTCh. 5 - Prob. 26PTCh. 5 - Prob. 1ECh. 5 - Prob. 2ECh. 5 - Prob. 3ECh. 5 - Prob. 4ECh. 5 - Prob. 5ECh. 5 - Prob. 6ECh. 5 - Prob. 1STPCh. 5 - Prob. 2STPCh. 5 - Prob. 3STPCh. 5 - Prob. 4STPCh. 5 - Prob. 5STPCh. 5 - Prob. 6STPCh. 5 - Prob. 7STPCh. 5 - Prob. 8STPCh. 5 - Prob. 9STPCh. 5 - Prob. 10STPCh. 5 - Prob. 11STPCh. 5 - Prob. 12STPCh. 5 - Prob. 13STPCh. 5 - Prob. 14STPCh. 5 - Prob. 15STPCh. 5 - Prob. 16STP

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