6
AssignmentDropdown

Factoring Polynomials: Double Grouping

Question 6 • Common Core Algebra I B-IC

Consider the trinomial x2 – 9x + 18. | Which pair of numbers has a product of ac and a sum of b? | What is the factored form of the trinomial?

Answer
A
(x + 3)(x + 6)
B
(x + 3)(x – 6)
C
(x – 3)(x + 6)
D
(x – 3)(x – 6)

Explanation

For x² − 9x + 18, a = 1, b = −9, and c = 18, so ac = 18. The numbers −3 and −6 have a product of 18 and a sum of −9. Splitting the middle term gives x² − 3x − 6x + 18, which factors as (x − 3)(x − 6), choice D.

AI-written and checked against the verified answer.