Find k so that x+2 is a factor of 2x^3-2kx^2-11x+5k.
I don't know to solve for k.
please help and thank you
You must be covering the factor theorem.
if x+2 is a factor of the f(x) , then f(-2) = 0
let f(x) = x^3-2kx^2-11x+5k
then f(-2) = -8 - 2k(4) + 22 + 5k = 0
solve for k
thanks
To find the value of k such that x + 2 is a factor of the polynomial 2x^3 - 2kx^2 - 11x + 5k, we need to use the remainder theorem. According to the theorem, if x + 2 is a factor of the polynomial, then when we substitute x = -2 into the polynomial, the result should be zero.
Let's substitute x = -2 into the polynomial and equate it to zero:
2(-2)^3 - 2k(-2)^2 - 11(-2) + 5k = 0
Now, let's simplify the equation:
2(-8) - 2k(4) + 22 + 5k = 0
-16 - 8k + 22 + 5k = 0
-16 + 22 + 14k = 0
6 + 14k = 0
Now, we can solve for k by isolating it on one side of the equation:
14k = -6
k = -6/14
k = -3/7
Therefore, the value of k that makes x + 2 a factor of 2x^3 - 2kx^2 - 11x + 5k is k = -3/7.