Use the Factor Theorem to determine whether g(x) is factor of f(x) in the following cases:
f(x) = 4x³ + 20x² + 33x + 18, g(x) = 2x + 3

Question

Use the Factor Theorem to determine whether g(x) is factor of f(x) in the following cases: f(x) = 4x 3 + 20x 2 + 33x + 18, g(x) = 2x + 3

Philoid · Accepted Answer

By Factor Theorem, we know that,

If p(x) is a polynomial and a is any real number, then g(x) = (x – a) is a factor of p(x), if p(a) = 0

For checking (2x + 3) to be a factor, we will find f(–3/2)

As, f(–3/2) is equal to zero, therefore, g(x) = (3x – 2) is a factor of f(x)

Use the Factor Theorem to determine whether g(x) is factor of f(x) in the following cases:f(x) = 4x3 + 20x2 + 33x + 18, g(x) = 2x + 3