Question

Factorise by using suitable identity
x^5-x

Answer 1

The factor of $x^{5} -x$ by using suitable identity is $x (x^{2} +1)(x+1) (x-1)$.

Step-by-step explanation:

Given:

$x^{5} -x$.

To Find:

The factor of $x^{5} -x$ by using suitable identity.

Identity Used:

$A^{2}-B^{2} =(A+B) (A-B)$  --------- Identity no.01.

Solution:

As given,$x^{5} -x$.actor of $x^{5} -x=x[x^{4} -1)]$

                           $=x [(x^{2} )^{2} -1^{2} ]$                  Using identity no.01.

                            $=x (x^{2} +1)[(x^{2} -1) ]$         Using identity no.01.

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

Thus,the factor of $x^{5} -x$ by using suitable identity is $x (x^{2} +1)(x+1) (x-1)$.

#SPJ2

Answer 2

Answer:

Using the suitable identity, the factors of $x^5-x$ is $x(x^2+1)(x+1)(x-1)$.

Step-by-step explanation:

Recall the identity,

$a^2-b^2=(a+b)(a-b)$ . . . . . (1)

Step 1 of 2

Consider the given equation as follows:

$x^5-x$

Take the term $x$ common from the given equation as follows:

⇒ $x(x^4-1)$ . . . . . (2)

Rewrite the obtained equation as follows:

⇒ $x((x^2)^2-1^2)$

Now,

Let $a=x^2$ and $b=1$.

Substitute the values $x^2$ for $a$ and 1 for $b$ in the identity (1) as follows:

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

$x^4-1=(x^2+1)(x^2-1)$

Step 2 of 2

Factoring the given equation.

Again, use the identity (1) to simplify further as follows:

$x^4-1=(x^2+1)(x+1)(x-1)$

Substitute the value of $x^4-1$ in the equation (2) as follows:

⇒ $x(x^2+1)(x+1)(x-1)$

Final answer: Using the suitable identity, the factors of $x^5-x$ is $x(x^2+1)(x+1)(x-1)$.

#SPJ2