Q. 3 - Precalculus Enhanced with Graphing Utilities

Question

Factor completely: $3x^4+6x^3+3x^2$

Step-by-Step Solution

Answer

The factors in the given expression is $3x^2(x+1{)}^2$

Step 1. Check for a common factor

The given expression is$3x^4+6x^3+3x^2$

Here we can see that the expression has a common factor, $3x^2$.

That is

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

Step 2. Write as a perfect square

Here, in the trinomial $x^2+2x+1$, the first term $x^2$ and the third term $1=1^2$are perfect squares. The middle term is  twice the product of $x$ and $1$ ,

Therefore, we have a perfect square.

Factoring the perfect square, we get the expression $(x+1{)}^2$

Hence,$3x^4+6x^3+3x^2=3x^2(x+1{)}^2$