Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

The factorization of the polynomial $x 5 + x 2$ is

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

x 2 (x + 1) x 2 − x − 1

x 2 (x + 1) x 2 + x + 1

x 2 (x − 1) x 2 − x + 1

x 2 (x + 1) x 2 − x + 1

answer is B.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The given polynomial is

x 5 + x 2 .

We start solving the given polynomial by taking the common.
Thus we have,

x 5 + x 2 = x 2 (x 3 + 1)

Since we know that

a 3 + b 3 = a + b (a 2 − a b + b 2),

therefore take

a = x 3 and b = 1.

Putting the values in the above formula, we get,

x 5 + x 2 = x 2 (x 3 + 1) = x 2 (x + 1) (x 2) - x 1 + 12

⇒ x 5 + x 2 = x 2 (x + 1) x 2 − x + 1

Therefore, the factorization of the polynomial

x 5 + x 2

x 2 (x + 1) x 2 − x + 1 .

Hence, option (2) is correct.

Watch 3-min video & get full concept clarity

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test