Question

Factor completely:$3x^4+6x^3+3x^2$

Short answer

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

Step-by-step solution

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 localid="1647515831673" $1=1^2$are perfect squares. The middle term is twice the product of localid="1647515850045" $x$and localid="1647515868323" $1$,

Therefore, we have a perfect square.

Factoring the perfect square, we get the expression localid="1647515891415" $(x+1{)}^2$

Hence,localid="1647515879792" $3x^4+6x^3+3x^2=3x^2(x+1{)}^2$