The polynomial 16x³+kx²-2x-5 has 2x+1 as one if its factors. Find k.
To find k, we can use the Factor Theorem, which states that if a polynomial f(x) has x - c as a factor, then f(c) = 0.
In this case, we are given that 2x + 1 is a factor of 16x³ + kx² - 2x - 5. Therefore, when we substitute x = -1/2 into the polynomial, the result should be 0.
Plugging x = -1/2 into the polynomial, we get:
16(-1/2)³ + k(-1/2)² - 2(-1/2) - 5 = 0
-8 + k/4 + 1 - 5 = 0
-12 + k/4 = 0
k/4 = 12
k = 48
Therefore, the value of k is 48.