# How do you factor x^5+2x^4+x^3?

May 27, 2018

You can take ${x}^{3}$ out, as follows:${x}^{3} \left({x}^{2} + 2 x + 1\right)$
This can be factored further: ${x}^{2} + 2 x + 1$ ==&gt; ${\left(x + 1\right)}^{2}$
so answer is: ${x}^{3} {\left(x + 1\right)}^{2}$

#### Explanation:

You can take${x}^{3}$ out, as follows:${x}^{3} \left({x}^{2} + 2 x + 1\right)$
This can be factored further: ${x}^{2} + 2 x + 1$ ==&gt; ${\left(x + 1\right)}^{2}$
so answer is: ${x}^{3} {\left(x + 1\right)}^{2}$

May 27, 2018

${x}^{3} {\left(x + 1\right)}^{2}$

#### Explanation:

color(blue)(x^5+2x^4+x^3

Factoring, means expressing the polynomial in terms of products of numbers or expressions. When we factor, we take the common terms inside the polynomials.

Take, ${x}^{3}$ out of the polynomial

$\rightarrow {x}^{3} \left({x}^{2} + 2 x + 1\right)$

We can further factor $\left({x}^{2} + 2 x + 1\right)$. It is in the form of color(brown)((a+b)^2=a^2+2ab+b^2.

So, ${x}^{2} + 2 x + 1$ can be written as ${x}^{2} + 2 \left(x\right) \left(1\right) + {1}^{2}$ Which equals color(brown)((x+1)^2

So, the final factored expression is written as

color(green)(rArrx^3(x+1)^2

Hope that helps!!.... $\phi$