Answer:
[tex]x(x+1)^2[/tex]
Step-by-step explanation:
Given:
The expression to factor is given as:
[tex]x^3+2x^2+x[/tex]
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:
[tex]x^3=x\times x\times x\\\\2x^2=2\times x\times x\\\\x=x[/tex]
Now, 'x' is a common factor for all the three terms. So, we factor it out. This gives,
[tex]x(\frac{x^3}{x}+2\frac{x^2}{x}+\frac{x}{x})\\\\x(x^2+2x+1)[/tex]
Now, we know a identity which is given as:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Here, [tex]x^2+2x+1[/tex] can be rewritten as [tex]x^2+2(1)(x)+1^2[/tex]
So, [tex]a=x\ and\ b=1[/tex]
Thus, [tex]x^2+2(1)(x)+1^2= (x+1)^2[/tex]
Therefore, the complete factorization of the given expression is:
[tex]x^3+2x^2+x=x(x+1)^2[/tex]
