Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Concept explainers

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

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Question

Chapter 4.6, Problem 16WE

To determine

To Find: Factor of polynomial $5v2+4v−1$

Expert Solution & Answer

Answer to Problem 16WE

Factor of polynomial $5v2+4v−1=(v+1)(5v−1)$

Explanation of Solution

Given information: polynomial $5v2+4v−1$

Formula used: If the quadratic trinomial $ax2+bx+c$ can be factored into the product $(px+q)(rx+s)$ where $p,q,r,s$ are integers, then

$ax2+bx+c=prx2+(ps+qr)x+qs$

Setting corresponding coefficients equal gives

$a=pr,b=ps+qr,c=qs$

Calculation:

polynomial $5v2+4v−1$

$pr=5$

The factorization begins

$(v )(5v )$

$qs=−1$

the coefficient of $v$ is positive.

$( 1)( −1)( −1)( 1 )$

There are some possible factorizations to check

$Trial Factorization Linear term of product (v+1)(5v−1) 4v (v−1)(5v+1) -4v$

Since the required linear term is $v$ , the first factorization is the correct one

$∴5v2+4v−1=(v+1)(5v−1)$

Chapter 4.6, Problem 15WE

Chapter 4.6, Problem 17WE

Chapter 4 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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