Question

Factor each polynomial.

$x^2-4x-21$

Short answer

The factors of the given polynomial are $(x+3)(x-7)$.

Step-by-step solution

Step 1. Compare.

Compare a given trinomial to $a{x}^2+bx+c$and write the values of $a,b$and role="math" localid="1647519883705" $c$.

$$\begin{gathered} a=1 \\ b=-4 \\ c=-21 \end{gathered}$$

Step 2. List the factors.

List the factors of $-21$, where one factor of each pair is negative. Look for the pair of factors with a sum of $-4$.

Factors of$-21$	Sum of factors
$1,-21$	$-20$
$3,-7$	$-4$

Therefore, the correct factors are 3 and $-7$.

Step 3. Apply factoring pattern of ax2+bx+c.

There are two numbers having product of $-21$and sum of $-4$. The numbers are 3 and $-7$.

role="math" localid="1647520367081" $$\begin{gathered} x^2-4x-21=\left(x+m\right)\left(x+p\right) \\ =\left(x+3\right)\left(x-7\right) \end{gathered}$$

Therefore, the factors of $x^2-4x-21$are $\left(x+3\right)\left(x-7\right)$.