Question

Using Remainder Theorem, find the value of $$k$$ if on dividing $$2x^3 + 3x^2 - kx + 5$$ by $$(x - 2)$$, leaves a remainder 7.

Answer 1

By the Remainder Theorem, the remainder is

$$f(2) = 2(2)^3 + 3(2)^2 - 2k + 5$$

$$= 33 - 2k$$

Since the remainder is $$7$$,

$$33 - 2k = 7$$

$$\Rightarrow 2k = 26$$

$$\Rightarrow k = 13$$