Question

Factor the polynomial and use the fac P(x)=x^(3)-x^(2)-12x.

Answer 1

To factor the polynomial P(x) = x^3 - x^2 - 12x, you start by factoring out the GCF, which is x, and then factor the quadratic to get the completely factored form P(x) = x(x - 4)(x + 3).

Step-by-step explanation:

To factor the polynomial P(x) = x3 - x2 - 12x, we can follow a step-by-step process:

1. First, factor out the greatest common factor (GCF). In this case, the GCF is x. So, we get P(x) = x(x2 - x - 12).
2. Next, we need to factor the quadratic equation inside the parentheses. We are looking for two numbers that multiply to -12 and add to -1 (the coefficient of x). These numbers are -4 and 3.
3. Now, we can write the factored form: P(x) = x(x - 4)(x + 3).

This shows that the polynomial has been factored completely. Notice that P(x) can also be easily graphed using a graphing calculator, and solutions or roots of the equation can be estimated with it.