Question

Factor x3 + 2x2 + x completely. (x + 1)2 x(x2 + 1) x(x + 1)2

Answer 1

x(x+1)^2

Explanation:

Answer 2

`x(x+1)^2`

Explanation:

Given:

The expression to factor is given as:

`x^3+2x^2+x`

In order to factor it, we write the factors of each of the terms of the given polynomial. So,

The factors of the three terms are:

`x^3=x* x* x\\\\2x^2=2* x* x\\\\x=x`

Now, 'x' is a common factor for all the three terms. So, we factor it out. This gives,

`x((x^3)/(x)+2(x^2)/(x)+(x)/(x))\\\\x(x^2+2x+1)`

Now, we know a identity which is given as:

`(a+b)^2=a^2+2ab+b^2`

Here,
`x^2+2x+1` can be rewritten as
`x^2+2(1)(x)+1^2`

So,
`a=x\ and\ b=1`

Thus,
`x^2+2(1)(x)+1^2= (x+1)^2`

Therefore, the complete factorization of the given expression is:

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