# How do you factor x^3 - 3x^2 = 0?

Jul 20, 2018

${x}_{1} = {x}_{2} = 0$ and ${x}_{3} = 3$

#### Explanation:

${x}^{3} - 3 {x}^{2} = 0$

${x}^{2} \cdot \left(x - 3\right) = 0$

Hence ${x}_{1} = {x}_{2} = 0$ and ${x}_{3} = 3$

Jul 20, 2018

The 2 factors are ${x}^{2}$ and $\left(x + 3\right)$
because ${x}^{2} \cdot \left(x + 3\right) = {x}^{3} - 3 {x}^{2}$

#### Explanation:

Look for things that when multiplied together result in the terms shown in the equation (${x}^{3} + 3 {x}^{2}$ in this case).

A factor is something that will divide into all terms, and can be placed outside of brackets, to be multiplied with all terms inside the brackets.

Sometimes all factors have more than one term and are therefore in brackets.

Looking at the question, in this case $x$ is common to both terms, and in fact ${x}^{2}$ is common to both terms, so ${x}^{2}$ is a factor.

${x}^{3} + 3 {x}^{2} = {x}^{2} \cdot \left(x\right) + {x}^{2} \cdot \left(3\right) \text{ ...(} {x}^{2}$ is common to both terms)

$\text{ "= x^2*(x + 3)" ...(}$so put it outside brackets)

$\text{ }$

${x}^{2}$ and $\left(x + 3\right)$ are factors of (${x}^{3} - 3 {x}^{2}$)