Question

Determine the value of b if the polynomial bx^{​​​​​3}+9x²+4x-10 when divided by (x-3)leaves a remainder of -22

Answer 1

By the remainder theorem, when a polynomial P(x) is divided by (x-a) the remainder is P(a).
We have P(x) = . bx^{​​​​​3}+9x²+4x-10 and a = 3. So remainder = P(3)
= b(3)^{​​​​​3}+9(3)²+4(3)-10
= 27b + 9(9) +12 -10
= 27b+81+12-10
= 27b+83
We are given remainder = -22
Hence 27b + 83 = -22
27b = -105
b = -105/27
b = -35/9 Answer