Enter your answer and show all the steps that you use to solve this problem in the space provided. Write the polynomial in factored form. x3−3x2−10x
To factor the polynomial x^3 - 3x^2 - 10x, we need to look for common factors and use factoring techniques such as grouping and factoring by grouping.
First, let's look for any common factors. In this case, we see that there is an x term that can be factored out:
x(x^2 - 3x - 10)
Now, we need to factor the quadratic expression inside the parentheses, x^2 - 3x - 10. To do this, we can look for two numbers that multiply to -10 and add up to -3. The numbers -5 and 2 satisfy these conditions, so we can factor the quadratic:
x(x - 5)(x + 2)
Therefore, the polynomial x^3 - 3x^2 - 10x in factored form is x(x - 5)(x + 2).