Question

the polynomial \[-6x^3-55x^2+kx-16\] has factors x+8 and 3x+2. what is the value of k?

Answer 1

i guess the other factor must be \(-2x-1\)

Answer 2

expand
\[(x+8)(3x+2)(-x-1)=-6x^3-55x^2-58x-16\]

Answer 3

You know that evaluating the polynomial at x=root, the value of the polynomial will be 0. Use this to your advantage by evaluating
\[-6(-8)^3-55(-8)^2+k(-8)-16=0\] and solve for \(k\).