What is the value of k such that (x^3+kx^2-9x-36)/ (x+4) has a remainder of zero?

Question

What is the value of k such that
`(x^3+kx^2-9x-36)/ (x+4)` has a remainder of zero?

Answer 1

The value of k that makes the remainder zero when (x^3 + kx^2 - 9x - 36) is divided by (x + 4) is k = 4, as per the Remainder Theorem.

Step-by-step explanation:

The value of k such that (x^3+kx^2-9x-36)/(x+4) has a remainder of zero can be found using the Remainder Theorem. This theorem states that if a polynomial f(x) is divided by (x-c), then the remainder is f(c).

To find the value of k, we set x = -4 because we are dividing by (x+4), and solve for k in the equation

((-4)^3+k(-4)^2-9(-4)-36=0).

So, the equation simplifies to (-64+16k+36-36=0), which further simplifies to (16k-64=0).

Solving for k gives us k=4.