Question

Show that (x + 2) is a factor of f(x) = x³ + 4x² + x – 6.

Answer 1

1. Identify the value of c:

Set the binomial equal to zero:

x + 2 = 0

⇒ x = –2

Therefore, c = –2.

2. Substitute x = –2 into the polynomial f(x):

f(–2) = (–2)³ + 4(–2)² + (–2) – 6

3. Simplify the terms:

(–2)³ = – 8

4(–2)² = 4(4) = 16

+(–2) = –2

4. Calculate the final result:

f(–2) = –8 + 16 – 2 – 6

f(–2) = 8 – 2 – 6

f(–2) = 0

Since f(–2) = 0, the remainder is zero. By the Factor Theorem, (x + 2) is ) verified as a factor of x³ + 4x² + x – 6.