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Question

Using remainder theorem, find the value of m if the polynomial ​
f(x)=x3+5x2mx+6 leaves a remainder 2m when divided by (x-1).

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Solution

Given: f(x)=x3+5x2mx+6, divisor = (x-1), and
remainder = 2m

From remainder theorem, we know that
when a polynomial f(x) is divided by (x-a), the
remainder is f(a).

f(1)=2m
(1)³+5(1)²m(1)+6=2m
1+5m+6=2m
3m=12
m=4

Hence, the value of m is 4.

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