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Consider this expression:
[tex]\[ x^2 + x - 72 \][/tex]

Replace the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] to rewrite the given expression:
[tex]\[ (x + a)(x + b) \][/tex]

Sagot :

GinnyAnswer
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]
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