Question

Determine the value of k, such that (x+3) is a factor of the polynomial f(x) =2x^3+ 11x^2+ kx+ 6

Answer 1

Let f(x) = 2x^3+ 11x^2+ kx+ 6

And q(x) = x+3

So, the zero of the polynomial will be
X+3=0

So, x = -3

-3 is the zero of the polynomial

Putting -3 instead of x

2(-3)^3 + 11(-3)^2 + k(-3) + 6 = 0
2 × -27 + 11 × 9 - 3k + 6 = 0
-54 + 99 -3k + 6 = 0
-3k +51 = 0
-3k = -51
3k = 51
k = 51/3
k = 17

So, the value of k is 17

Hope it helps