Question

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

Answer 1

Answer:

$x(x+1)^2$

Step-by-step 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:

$x^3=x\times x\times x\\\\2x^2=2\times x\times x\\\\x=x$

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

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

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:

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

Answer 2

Answer:

x(x+1)^2

Step-by-step explanation: