Question

A polynomial in $$x$$ is $$x^3 + 5x^2 - kx - 24$$. 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:

With $$k = 2$$, $$f(-4) = -64 + 80 + 8 - 24 = 0$$, so the Factor Theorem gives $$(x + 4)$$.