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1. Factor the following polynomials using the factor theorem. (a) x³-4x²+x+6 (b) x³+8x²+21x+18 (c) x-x³-3x²+x+2

1. Factor the following polynomials using the factor theorem. (a) x³-4x²+x+6 (b) x³+8x²+21x+18 (c) x-x³-3x²+x+2

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. Factor the following polynomials using the factor theorem. (a) x³-4x²+x+6 (b) x³+8x²+21x+18 (c) x4-x³-3x²+x+2 2. Factor each expression (a) x³-8 (b) 27x³+1 (c) 625x³-40 (d) 125-64x³ 3. Factor fully. a. abx³+(a+b-ab)x²+(1-a-b)x-1 [note P(1)=0 ] b. x³-(p+q-r)x²+(pq-pr-qr)x+pqr [note P(p)=P(q)=P(-r)=0] 4. The factors of 5x²+kxy-6y²+13x-5y+6 are of the form (ax+by+c)(dx+ey+f), where a,b,c,d,e,f are integers. Find the value of k. 5. Factor x¹²-1 fully. 6. List all polynomials of the form x++bx³+cx²+dx+e with rational coefficients that are factors of the polynomial, x¹²-1.
Transcribed Image Text:1. Factor the following polynomials using the factor theorem. (a) x³-4x²+x+6 (b) x³+8x²+21x+18 (c) x4-x³-3x²+x+2 2. Factor each expression (a) x³-8 (b) 27x³+1 (c) 625x³-40 (d) 125-64x³ 3. Factor fully. a. abx³+(a+b-ab)x²+(1-a-b)x-1 [note P(1)=0 ] b. x³-(p+q-r)x²+(pq-pr-qr)x+pqr [note P(p)=P(q)=P(-r)=0] 4. The factors of 5x²+kxy-6y²+13x-5y+6 are of the form (ax+by+c)(dx+ey+f), where a,b,c,d,e,f are integers. Find the value of k. 5. Factor x¹²-1 fully. 6. List all polynomials of the form x++bx³+cx²+dx+e with rational coefficients that are factors of the polynomial, x¹²-1.
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