What is 3x2 + 21x + 18 in factored form?

0

A

3 (x + 2) (x + 3)

O

B. 3 (x + 6) (x + 1)

0

C. 3 (x + 3) (x + 2)

D. 3 (x + 1) (x + 2)

B

Step-by-step explanation:

Given

3x² + 21x + 18 ← factor out 3 from each term

= 3 (x² + 7x + 6) ← factor the quadratic

Consider the factors of the constant term ( + 6) which sum to give the coefficient of the x - term ( + 7)

The factors are + 6 and + 1, since

6 * 1 = 6 and 6 + 1 = 7, thus

x² + 7x + 6 = (x + 6) (x + 1)

Thus

3x² + 21x + 18 = 3 (x + 6) (x + 1) → B