To solve the given expression [tex]\( x^2 + x - 72 \)[/tex] by factoring, we need to find two numbers [tex]\( a \)[/tex] and [tex]\( b \)[/tex] such that:
1. Their product is equal to the constant term, which is [tex]\(-72\)[/tex].
2. Their sum is equal to the coefficient of the linear term, which is [tex]\( 1 \)[/tex].
After analyzing, we determine that the numbers [tex]\( 9 \)[/tex] and [tex]\(-8\)[/tex] satisfy these conditions:
- [tex]\( 9 \times (-8) = -72 \)[/tex]
- [tex]\( 9 + (-8) = 1 \)[/tex]
Therefore, we can rewrite the expression [tex]\( x^2 + x - 72 \)[/tex] in the factored form as:
[tex]\[
(x + 9)(x - 8)
\][/tex]
In corresponding to the expression [tex]\( (x + a)(x + b) \)[/tex]:
- [tex]\( a = 9 \)[/tex]
- [tex]\( b = -8 \)[/tex]
So, the correct values to replace in the expression [tex]\( (x + a)(x + b) \)[/tex] are [tex]\( a = 9 \)[/tex] and [tex]\( b = -8 \)[/tex].
The boxed answer is:
[tex]\[
(x + 9)(x - 8)
\][/tex]
