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Question

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division.

f(x) = x43x2+4, g(x) = x - 2

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Solution

Given: f(x) = x43x2 + 4, g(x) = x - 2

We know that,

Remainder theorem formula is: p(x)=(xc)q(x)+r(x)

p(x)(xc)q(x)=r(x)

So, using g(x)

x2=0 x=2

Remainder =f(x)(x2)

=x43x2+4(x2)

=(2)43(2)2+4

=1612+4

=2012

=8

Now, verify using actual division:


Remainder = 8


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