Question

A polynomial in x is x³ + 5x² – kx – 24. Which of the following is a factor of the given polynomial so that the value of k is 2?

Options

• (x + 2)

• (x – 3)

• (x + 4)

• (x – 4)

Answer 1

(x + 4)

Explanation:

By the factor theorem, (x + 4) is a factor exactly when f(–4) = 0.

For f(x) = x³ + 5x² – kx − 24,

f(–4) = (–4)³ + 5(–4)² – k(–4) – 24

= –64 + 80 + 4k – 24

= 4k – 8

Set 4k – 8 = 0

⇒ 4k = 8

⇒ k = 2

Thus, (x + 4) is the factor that gives k = 2.