Question

Factor out the common factor.

$3x^4-6x^3-x^2$

Short answer

The solution$3x^4-6x^3-x^2=x^2\left(3x^2-6x-1\right)$

Step-by-step solution

Step 1. Apply the concept of polynomials.

Apolynomial in the variable x is an expression of the form$a_n{x}^n+a_{n-1}{x}^{n-1}+a_{n-2}{x}^{n-2}+\mathrm{...}+a_{1}x+a_0$

$a_n,a_{n-1},a_{n-2},\mathrm{...},a_1,a_0$are real numbers, and n is a nonnegative integer. If $a_n\ne 0$, then the polynomial hasdegree n. The monomials $a_k{x}^k$that make up the polynomial are called theterms of the polynomial.

Step 2. Analyze the polynomial.

Given$3x^4-6x^3-x^2$

We arrange the terms of the polynomial such the exponents are in descending order.

$3x^4-6x^3-x^2$

Step 3. Find the greatest common factor.

$3x^4-6x^3-x^2$is the polynomial

$3,-6$and $-1$have greatest common factor 1

$x^4,x^3,x^2$have greatest common factor$x^2$

So, the greatest common factor of the two terms is$x^2$

Step 4. Factor the polynomial.

Now, the factors of polynomial$3x^4-6x^3-x^2$are given by:

$3x^4-6x^3-x^2=x^2\left(3x^2-6x-1\right)$