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Question

If the given polynomial f(x)=x4+ax3−5x2+7x−6, is divided by x−3 and leaves remainder as −3 then the value of a is

A
-2.0
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B
-02
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C
-2
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D
-2.00
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Solution

Given: f(x)=x4+ax35x2+7x6.

Remainder Theorem states that if a polynomial p(x) is divided by xa, then the remainder obtained is p(a)

On dividing f(x) by x3, the remainder obtained will be:
f(3)=(3)4+a(3)35(3)2+7(3)6=3
f(3)=81+27a45+216=3
27a=54
a=2

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