Chapter 8, Problem 21PT

To determine

To Find: List the factors of the given polynomial.

Answer to Problem 21PT

The factor of the polynomial $15x^2+7x-2$ are $(5x-1)(3x+2)$ .

Explanation of Solution

Given information:

  $15x^2+7x-2$

Consider the polynomial $15x^2+7x-2$ .

The product of $15x^2$ term and constant term is $15x^2\times (-2)=-30x^2$ .

The middle term of the polynomial is $7x$ .

Consider $(x+m)(x+p)$ be the factor of the polynomial $15x^2+7x-2$ .

The coefficient of product of $x^2$ term and constant term is negative and coefficient of middle term of the polynomial is also positive. Thus, the value of m and p, one positive and one negative.

Calculate the value of m and p as,

Factors of $30:(-1,30),(-2,15),(-3,10),(-5,6)$

m of factors: $29,13,7,1$

  $15x^2+7x-2=15x^2-3x+10x-2$ . The correct factors are 10 and −3

  $=(5x-1)(3x+2)$

Therefore, the factor of the polynomial $15x^2+7x-2$ are $(5x-1)(3x+2)$ .