How do you determine the value of k if the remainder is 3 given #(x^3+kx^2+x+5) div(x+2)#?

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Answer 1 · 2017-02-13T15:39:03

The answer is #k=2#

Let #f(x)=x^3+kx^2+x+5#

When #f(x)# is divided by #(x+2)# , the remainder is #=3#

This is the remainder theorem

so,

#f(-2)=-8+4k-2+5=3#

#4k=3+5 =8#

#k=2#