Question

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

Answer 1

You can take `x^3` out, as follows:`x^3(x^2+2x+1)`
This can be factored further: `x^2+2x+1` ==> `(x+1)^2`
so answer is: `x^3(x+1)^2`

Explanation:

You can take`x^3` out, as follows:`x^3(x^2+2x+1)`
This can be factored further: `x^2+2x+1` ==> `(x+1)^2`
so answer is: `x^3(x+1)^2`

Answer 2

`x^3(x+1)^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

`rarrx^3(x^2+2x+1)`

We can further factor `(x^2+2x+1)`. It is in the form of `color(brown)((a+b)^2=a^2+2ab+b^2`.

So, `x^2+2x+1` can be written as `x^2+2(x)(1)+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`