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Division Algorithm for a Polynomial

If the polyno...

Question

If the polynomial $x^{4} + 2 x^{3} + 8 x^{2} + 12 x + 18$ is divided by another polynomial $x^{2} + 5,$ then the remainder comes out to be ax + b. The value of 2a + 3b is

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Solution

The correct option is C 13
Given that the polynomial $x^{4} + 2 x^{3} + 8 x^{2} + 12 x + 18$ when divided by $x^{2} + 5,$ leaves the remainder ax + b.

Dividing $x^{4} + 2 x^{3} + 8 x^{2} + 12 x + 18 b y x^{2} + 5, we get$

Given that the remainder is ax + b.

∴ a = 2 and b = 3

∴ 2a + 3b = 2 × 2 + 3 × 3 = 4 + 9 = 13

Hence, the correct answer is option (c).

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