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Question

If the polynomial x4+2x3+8x2+12x+18 is divided by another polynomial x2+5, then the remainder comes out to be ax + b. The value of 2a + 3b is

A
12
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B
11
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C
13
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D
18
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Solution

The correct option is C 13
Given that the polynomial x4+2x3+8x2+12x+18 when divided by x2+5, leaves the remainder ax + b.

Dividing x4+2x3+8x2+12x+18 by x2+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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