Question

In the following exercises, factor.

$5x^3-3x^2+5x-3$.

Short answer

The factors for the expression $5x^3-3x^2+5x-3$ are,$\left(5x-3\right)\left(x^2+1\right)$.

Step-by-step solution

Given expression is,

$5x^3-3x^2+5x-3$.

The objective is, we need to find the factor for the given expression.

First group each term with the common factors.

$5x^3-3x^2+5x-3=\left(5x^3-3x^2\right)+\left(5x-3\right)$

Now factor out the common terms.

$$\begin{gathered} 5x^3-3x^2+5x-3=x^2\left(5x-3\right)+1\left(5x-3\right) \\ =\left(x^2+1\right)\left(5x-3\right) \end{gathered}$$

The obtained factors are,$\left(x^2+1\right)\left(5x-3\right)$.

Step 3 let us check the answer by multiplying the factors.

$$\begin{gathered} \left(5x-3\right)\left(x^2+1\right)=5x^3+5x-3x^2-3 \\ =5x^3-3x^2+5x-3 \end{gathered}$$

which is true.