Chapter 4.3, Problem 27PPS

To determine

To calculate: The factors of the polynomial $x^2-9x-22$ .

Answer to Problem 27PPS

The polynomial is factored as $\left(x-11\right)\left(x+2\right)$ .

Explanation of Solution

Given information:

The polynomial $x^2-9x-22$ .

Formula used:

To factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

Calculation:

Consider the polynomial $x^2-9x-22$ .

Recall that to factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

For the above polynomial $-11$ and $2$ are two numbers such that their sum is $-9$ and product is $-22$ .

Apply it, first the group the similar terms,

  $\begin{array}{c}{x}^2-9x-22=x^2-11x+2x-22\\ =x\left(x-11\right)+2\left(x-11\right)\\ =\left(x-11\right)\left(x+2\right)\end{array}$

Thus, the polynomial is factored as $\left(x-11\right)\left(x+2\right)$ .