Factor x3 + 2x2 + x completely.a. (x+1)^2b. x(x+1)^2c. x(x+1)^2

Accepted Solution

Option B ANSWER:  The factors of  [tex]$x^{3}+2 x^{2}+x$[/tex] is [tex]$x(x+1)^{2}$[/tex]SOLUTION: Given, cubic expression is  [tex]$x^{3}+2 x^{2}+x$[/tex]Now, we have to find the factors of above equation. To factorize the given equation, follow the below steps: [tex]$\mathrm{x}^{3}+2 \mathrm{x}^{2}+\mathrm{x}$[/tex]Since x is common in every term of expression, we can take it as common[tex]$x\left(x^{2}+2 x+1\right)$[/tex]“2x” can be rewritten as “x + x”, the above equation becomes,[tex]$x\left(x^{2}+x+x+1\right)$[/tex]Taking the common terms out of bracket. we getx(x (x + 1) + 1 (x + 1))  Taking (x + 1) as common., we getx ((x + 1)(x + 1))  [tex]$x(x+1)^{2}$[/tex]Hence, the second option b is correct.