Question

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)

Answer 1

B

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