Given that f(x)=x^3+4x^2+bx+c. When *f* is divided by (x-3), the remainder is 110. In addition, when *f* is divided by (x+2), the remainder is 150. The sum of b+c=?

1 Answer
Oct 1, 2017

Given that f(x)=x^3+4x^2+bx+c. When f is divided by (x-3), the remainder is 110.
So we have f(3)=110

=>3^3+4*3^2+3b+c=110

=>3b+c=47......[1]

In addition, when f is divided by (x+2), the remainder is 150.

This means

f(-2)=150

=>(-2)^3+4*(-2)^2-2b+c=150

=>-2b+c=142.......[2]

Subtracting [2] from [1] we get

5b=-95

=>b=-19

Inserting b=-19 in [1] we get

3*(-19)+c=47

=>c=104

So the sum of b+c=104-19=85