Determine the value of k such that x+2 is a factor of p(x)= x^4-3x^3+kx^2-x+6

Question

someone pls help me 😢 I have to finish my thanksgiving packet LMAO

Answer 1

x - c is a factor of a polynomial function f(x) if f(c) = 0.

So, x + 2 = x - (-2) is a factor of p(x) when p(-2) = 0.

(-2)⁴ - 3(-2)³ + k(-2)²- (-2) + 6 = 0

16 + 24 + 4k + 8 = 0

4k = -48

k = -12