Question

Use the given factors to write the complete factorization of the function: f(x) = x^4 + 2x^3 - 13x^2 – 38x - 24.

Given: (x+3) and (x-4) are factors.

Answer 1

To write the complete factorization of the function f(x), divide the function by the given factors (x+3) and (x-4) using synthetic division, and continue to divide the resulting quotient by (x-4) to find the remaining factors.

Step-by-step explanation:

To write the complete factorization of the function f(x) = x^4 + 2x^3 - 13x^2 – 38x - 24, we can use the given factors (x+3) and (x-4) to find the remaining factors.

We can start by dividing the function by (x+3) using synthetic division. The remainder should be 0 for (x+3) to be a factor. If the remainder is 0, the quotient obtained will be a quadratic function.

Next, we can divide the quotient obtained by (x-4) to find the remaining factors. If the remainder is 0, the quotient will be a linear function.

By factoring the function completely, we will have the complete factorization of the function.