## Precalculus: Mathematics for Calculus, 7th Edition

The greatest common factor in the expression 3$x^{3}$ + $x^{2}$ is $x^{2}$, and the expression factors as $x^{2}$(3x + 1)
If one term is a factor of the other, then by definition it must be the greatest common factor of the two. $x^{2}$ is a factor of 3$x^{3}$, as 3$x^3$ is equivalent to 3x $\times$ x$^2$, therefore the greatest common factor is x$^2$. To find what the expression factors to, you now divide each term by x$^2$, set this in parenthesis, and put x$^2$ outside the parenthesis. This gives x$^2$(3x + 1)