Question

the polynomial p(x)=kx^3+9x^2+4x-8when divided by x+3 leaves a remainder -20.find the value of k

Answer 1

p(x) = kx³ + 9x² + 4x - 8

P(-3) = k(-3)³ + 9(-3)² + 4(-3) - 8 = -20

k(-27) + 9(9) + (-12) - 8 = -20

-27k + 81 - 12 - 8 = -20

-27k + 81 - 20 = -20

-27k + 61 = -20

-27k = -61 - 20

-27k = -81

k = $\frac{-81}{-27}$

k = 3

therefore k = 3.