Using Remainder Theorem, find the value of k if on dividing 2x³ + 3x² - kx + 5 by (x - 2), leaves a remainder 7.
Factorisation
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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.

KnowledgeBoat · Accepted Answer

By remainder theorem,

If f(x) is divided by (x - a), then remainder = f(a).

Let f(x) = 2x³ + 3x² - kx + 5

Given,

Remainder = 7

Divisor :

⇒ x - 2 = 0

⇒ x = 2

Substituting x = 2 in f(x), gives remainder 7.

⇒ f(2) = 7

⇒ 2(2)³ + 3(2)² - k(2) + 5 = 7

⇒ 2(8) + 3(4) - 2k + 5 = 7

⇒ 16 + 12 - 2k + 5 = 7

⇒ -2k + 33 = 7

⇒ 2k = 33 - 7

⇒ 2k = 26

⇒ k = $\dfrac{26}{2}$

⇒ k = 13.

Hence, the value of k is 13.

Mathematics