Question

enter the correct answer in the box. what is the factored form of this expression? $x^2 - 121$ fill in the values for $p$ and $q$ to complete the factored form of the expression. $(x + p)(x + q)$

Explanation:

Step1: Recognize difference of squares

The expression $x^2 - 121$ is a difference of two perfect squares, since $121 = 11^2$, so it fits $a^2 - b^2$.

Step2: Apply difference of squares formula

Use the identity $a^2 - b^2=(a+b)(a-b)$. Substitute $a=x$, $b=11$:
$x^2 - 11^2=(x+11)(x-11)$

Step3: Match to $(x+p)(x+q)$

Rewrite $(x-11)$ as $(x+(-11))$, so $p=11$ and $q=-11$ (or vice versa).

Answer:

$p=11$, $q=-11$, so the factored form is $(x+11)(x-11)$