Question

the polynomial 24x^3+mx^2-16x-6 has factors 3x+1 and 2x+2. determine the value of m

Answer 1

(3x+1)(2x+2)(4x+k) = 24x^3 + (6k+32)x^2 + (8k+8)x + 2k

so 2k = -6 ==> k = -3
(3x+1)(2x+2)(4x-3) = 24x^3+14x^2-16x-6
so m=14