The polynomial p(x) =6x^3+2x^2-ax+b when divided by x+1 leaves remainder 14. Also x-1 is a factor of p(x). Find the value of a and b.

Answer 1

When divided by x+1, the remainder is 14.

So, p(-1) = 14.

Then

-6 + 2 + a + b = 14

a + b - 4 = 14

a + b = 18

Likewise, since x-1 is a factor, f(1) = 0.

So then, 6 + 2 - a + b = 0

b - a + 8 = 0

b - a = -8

a - b = 8

a + b = 18

a - b = 8

means that 2a = 26

a = 13--> b = 5

p(x) = 6x^3 + 2x^2 - 13x + 5