Write the polynomial in factored form.
x^3 - 3x^2 - 10x
The polynomial x^3 - 3x^2 - 10x can be factored as:
x(x^2 - 3x - 10)
We can further factor the quadratic expression x^2 - 3x - 10 using the quadratic formula or by factoring the expression:
x^2 - 3x - 10 = (x - 5)(x + 2)
Therefore, the polynomial x^3 - 3x^2 - 10x can be written in factored form as:
x(x - 5)(x + 2)
can you elaborate more on how to get that answer
Certainly! To factor the polynomial x^3 - 3x^2 - 10x, we look for the common factor that all the terms share, which is x:
x^3 - 3x^2 - 10x = x(x^2 - 3x - 10)
Now, we need to factor the quadratic expression x^2 - 3x - 10. This can be done by finding two numbers, let's call them a and b, such that their product is ac = -10 (the product of the coefficient of x^2 and the constant term) and their sum is b = -3 (the coefficient of x). In this case, a = -5 and b = 2 fit these conditions:
x^2 - 3x - 10 = (x - 5)(x + 2)
Therefore, the polynomial x^3 - 3x^2 - 10x can be fully factored as:
x(x - 5)(x + 2)