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

Question

Titan

Mathematics

9 May, 15:44

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

+4

Answers (2)

Know the Answer?

Ean Vaughan · Answer 1

B=-5

C=3

Step-by-step 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)