1. Factor the following polynomials using the factor theorem.(a) x³-4x²+x+6(b) x³+8x²+21x+18(c) x4-x³-3x²+x+22. Factor each expression(a) x³-8(b) 27x³+1(c) 625x³-40(d) 125-64x³3. 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 factorsof the polynomial, x¹²-1.

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Answered: 1. Factor the following polynomials…

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Algebra

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 & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 1DE

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Question

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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