Question

Express the polynomial as a product of linear factors.

1x) = 3x^3+12x^2 + 3x - 18
O A. (x-2)(x+3)(x-3)
O B. (x+3)(x + 6)(x - 1)
O c. 3(x - 1)(x+3)(x+2)
D. (x-3)(x + 3)(x - 2)

Answer 1

C

Explanation:

Given

3x³ + 12x² + 3x - 18

The sum of the coefficients = 3 + 12 + 3 - 18 = 0

Thus x = 1 is a root and (x - 1) is a factor

Divide 3x³ + 12x² + 3x - 18 by (x - 1) using Synthetic division

1 | 3 12 3 - 18

↓ 3 15 18

-----------------------------

3 15 18 0 ← remainder

Quotient = 3x² + 15x + 18 = 3(x² + 5x + 6)

Thus

3x³ + 12x² + 3x - 18 = 3(x - 1)(x² + 5x + 6) = 3(x - 1(x + 3)(x + 2) → C