Question

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

Answer 1

Option B

ANSWER:  

The factors of  $x^{3}+2 x^{2}+x$ is $x(x+1)^{2}$

SOLUTION:

Given, cubic expression is  $x^{3}+2 x^{2}+x$

Now, we have to find the factors of above equation.

To factorize the given equation, follow the below steps:

$\mathrm{x}^{3}+2 \mathrm{x}^{2}+\mathrm{x}$

Since x is common in every term of expression, we can take it as common

$x\left(x^{2}+2 x+1\right)$

“2x” can be rewritten as “x + x”, the above equation becomes,

$x\left(x^{2}+x+x+1\right)$

Taking the common terms out of bracket. we get

x(x (x + 1) + 1 (x + 1))  

Taking (x + 1) as common., we get

x ((x + 1)(x + 1))  

$x(x+1)^{2}$

Hence, the second option b is correct.