Factor the trinomial completely.
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A) b(ab - 9)(a + 7)
B) (ab + 9)(ab - 7)
C) (ab - 9)(ab + 7)
D) b(ab + 9)(a - 7)

Question

Factor the trinomial completely.
-
A) b(ab - 9)(a + 7) 
B) (ab + 9)(ab - 7) 
C) (ab - 9)(ab + 7) 
D) b(ab + 9)(a - 7)

Quizplus · Accepted Answer

The trinomial can be rewritten as ab^2 - 9ab + 7ab - 63 = ab(ab - 9) + 7(ab - 9) = (ab - 9)(ab + 7) To factor a trinomial of the form ab^2 + cb + d, we want to find two numbers that multiply to d and add to c. In this case, d is 63 and c is 1. The only two numbers that satisfy these conditions are 9 and 7 (9*7=63 and 9+7=16). So we can write the trinomial as:

ab^2 + 9ab + 7ab + 63

Now we can factor by grouping:

(ab^2 + 9ab) + (7ab + 63)

ab(ab + 9) + 7(ab + 9)

(ab+7)(ab+9)

But we can also write this as (ab+9)(ab+7), which matches choice C. Therefore, the answer is C, (ab - 9)(ab + 7).

Factor the Trinomial Completely