Write the polynomial in factored form. x^3−3x^2−10x

x(x + 2)(x - 5)

show the steps

To factor the polynomial x^3 - 3x^2 - 10x, we can first look for common factors, which in this case is x.

Step 1: Factor out x from the polynomial:
x(x^2 - 3x - 10)

Step 2: Factor the quadratic expression x^2 - 3x - 10:
We need to find two numbers that multiply to -10 and add up to -3. These numbers are -5 and 2.
(x - 5)(x + 2)

Therefore, the factored form of the polynomial x^3 - 3x^2 - 10x is x(x - 5)(x + 2).