Chapter 8, Problem 22PT

To determine

To Evaluate: Factorise the given polynomial.

Answer to Problem 22PT

The factor of the polynomial $x^2-25$ are $(x-5)(x+5)$

Explanation of Solution

Given information:

  $x^2-25$

Consider the polynomial $x^2-25$ .

The product of $x^2$ term constant term is $x^2\times (-25)=-25x^2$ .

The middle term of the polynomial is 0.

Consider $(x+m)(x+p)$ be the factor of the polynomial $x^2-25$ .

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

Calculate the value of $\text{m}$ and $p$ as,

Factors of $-25$  Sum of Factors

  $1,-25$      -24

  $5,-5$       0

  $x^2-25=(x-5)(x+5)$ The correct factors are 5 and −5

Therefore, the factor of the polynomial $x^2-25$ are $(x-5)(x+5)$ .