Question

When the polynomial x^4-3x^3-7x^2+7x+2 is divided by x+2 the quotient is x^3 +Bx^2 +Cx +1. Find the value of B +C

Answer 1

B=-5

C=3

Explanation:

x^4-3x^3-7x^2+7x+2= x^4-3x^3-10x^2+3x^2+7x+2

=x^4-3x^3-10x^2+ 3x^2+7x+2

=x^2(x^2-3x-10)+ 3x^2+7x+2

=x^2(x^2+2x-5x-10)+ 3x^2+6x+x+2

=x^2(x(x+2)-5(x+2))+ 3x(x+2)+1(x+2)

=(x+2)(x^2(x-5)+(3x+1))

=(x+2)(x^3-5x^2+3x+1)

Answer 2

B=-5

C=3

Explanation: