Question

When x³-2x^2-15x is factored completely, which expression is one of the factors?

A. X-5
B. x + 5
C. x2 – 5x
D. x2-2x-15

Answer 1

When x³-2x^2-15x is factored completely, one of the factors is x-5.

To factor the expression, we can use the method of grouping. We can rewrite the expression as follows:

x³-2x^2-15x = (x³-2x^2) - 15x

We can then factor the first two terms using the difference of squares:

x³-2x^2-15x = (x-2)(x^2+2x) - 15x

We can then factor the last term using the difference of squares:

x³-2x^2-15x = (x-2)(x^2+2x) - (5)(3x)

Then, we can combine the two factors to get the final answer:

x³-2x^2-15x = (x-5)(x^2+2x-3x)

The final factorization is:

x³-2x^2-15x = (x-5)(x^2-x)

So, the correct answer is (A) x-5.