Q. 345 - Intermediate Algebra

Question

In the following exercises, factor the greatest common factor from each polynomial.

$4x^3-12x^2+16x$

Step-by-Step Solution

Answer

The factored form of the polynomial is,

$4x(x^2-3x+4)$.

Step 1. Given Information

We are given a polynomial,

$4x^3-12x^2+16x$

Step 2. Finding the greatest common factor

Factoring the polynomial,

$4x^3-12x^2+16x=2\times 2\times x\times x\times x-2\times 2\times 3\times x\times x+2\times 2\times 2\times 2\times x$

The greatest common factor is $4x$,

$$\begin{gathered} 4x^3-12x^2+16x=4x\times x\times x-4x\times 3\times x+2\times 2\times 4x \\ 4x^3-12x^2+16x=4x(x^2-3x+4) \end{gathered}$$

Step 3. Checking the factorization

Multiplying the factors,

$$\begin{gathered} 4x(x^2-3x+4)=4x^3-12x^2+16x \\ 4x\times x^2-4x\times 3x+4x\times 4=4x^3-12x^2+16x \\ 4x^3-12x^2+16x=4x^3-12x^2+16x \\ LHS=RHS \end{gathered}$$

Hence the factorization is correct.