To rewrite the given expression [tex]\( x^2 + x - 72 \)[/tex] in the form [tex]\( (x + a)(x + b) \)[/tex], follow these steps:
1. Start with the original quadratic expression:
[tex]\[
x^2 + x - 72
\][/tex]
2. We want to factor this quadratic expression into the form:
[tex]\[
(x + a)(x + b)
\][/tex]
3. From the factors provided, it is known that:
[tex]\[
(x - 8)(x + 9)
\][/tex]
Therefore, the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are [tex]\( -8 \)[/tex] and [tex]\( 9 \)[/tex], respectively.
Replace [tex]\( a \)[/tex] and [tex]\( b \)[/tex] in the factorized form:
[tex]\[
(x - 8)(x + 9)
\][/tex]
So, the expression [tex]\( x^2 + x - 72 \)[/tex] is correctly written as:
[tex]\[
(x - 8)(x + 9)
\][/tex]
