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Question

Determine the value of m if (x-1) is a factor x3+5x2+mn+4.

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Solution

Let p(x)=x3+5x2+mx+4. Since (x-1) is a factor of p(x), the remainder p(1)=0. Now,
p(1)=0(1)3+5(1)2+m(1)+4=0
1+5+m+4=0
m+10=0
m=10

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