Question

Factor f(x) 3x^3-4x^2-28x-16 given that (x+2) is a factor

Answer 1

Step-by-step explanation:

3x³ - 4x² - 28x - 16

= (x + 2)(Ax² + Bx + C)

= Ax³ + (2A + B)x² + (2B + C)x + 2C.

By Comparing Coefficients, we have:

• A = 3,
• 2A + B = -4,
• 2B + C = -28,
• 2C = -16.

Solving them will give A = 3, B = -10 and C = -8.

Hence 3x³ - 4x² - 28x - 16

= (x + 2)(3x² - 10x - 8)

= (x + 2)(3x + 2)(x - 4).

The answer is f(x) = (x + 2)(3x + 2)(x - 4).