# How do you factor 6x^3 - 3x^2 + 9?

Jun 7, 2018

bolded text $3 \left(2 {x}^{3} - {x}^{2} + 3\right)$

#### Explanation:

1-Find the greatest number they have in common first.
Looking at the expression, there are three numbers: $3 , 6 , 9$. The GCF (greatest common factor) of these is $3$. Then we look at the greatest variable they have in common. There is only one variable, $x$. However, the $9$ does not have any $x$ attached to it, therefore we cannot factor out an $x$.

2-Now we have to take out a $3$. When we take out the $3$, we are kind of dividing everything by $3$, separately. For example, when you factor out $3$ from $6 {x}^{3}$, you get $2 {x}^{3}$ since you are basically just dividing the $6$ by $3$. Doing the same for $3 {x}^{2}$ and $9$, we get our answer:

3- $3 \left(2 {x}^{3} - {x}^{2} + 3\right)$

Side Note: (this is to help for future questions)
If we were just factoring $6 {x}^{3} - 3 {x}^{2}$, we would factor out $3 {x}^{2}$. This is because 3 is the largest common factor for the coefficients and both have x attached to them. But since the degree is not the same, we take the smaller degree of x so that both numbers can be divisible by it.