Chapter 8, Problem 22MCQ

To determine

To Evaluate: Factorise the given polynomial.

Answer to Problem 22MCQ

The factor of polynomial $x^2+4x-21$ are $(x-3)(x+7)$ .

Explanation of Solution

Given information:

  $x^2+4x-21$

The product of $x^2$ term and constant term is $x^2\times (-21)=-21x^2$ .

The middle term of the polynomial is $4x$ .

Consider $(x+m)(x+p)$ be the factor of the polynomial $x^2+4x-21$ .

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 factor with greater absolute value is also positive.

Calculate the value of $m$ and $p$ as,

Factors of -21 (-1,21), (-3,7)

Sum of factors: 20, 4

  $x^2+4x-21=(x+m)(x+p)$ The correct factors are −3 and 7

  $=(x-3)(x+7)$

Therefore, the factor of polynomial $x^2+4x-21$ are $(x-3)(x+7)$ .