AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Factorize the polynomial expression $1 + 2 x + x^{2}$ , and choose the correct option which represents the factored form correctly.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(x - 1) (x - 1)

(x + 2) (x - 1)

(x + 1) (x + 1)

(x + 1) (x - 1)

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

A polynomial expression

1 + 2 x + x^{2}

is given and it is asked to determine its factors.
To do so, we will have to use the method of middle-term splitting.
The given expression can be rearranged as follows,

x^{2} + 2 x + 1

.
To proceed with the factorization, we first need to find the product of the first and last terms of the given polynomial function, i.e.,

x^{2} \times 1 = x^{2}

.
Next, we need to split middle term of the polynomial expression, i.e.,

2 x

as a sum or difference of two terms, such that their product is equal to the product of first and last terms, i.e.,

x^{2}

x^{2} + 2 x + 1 \Leftrightarrow x^{2} + x + x + 1

Now, we need to group the terms and factor out the common factors, as follows,

\begin{matrix} (x^{2} + x) + (x + 1) = x (x + 1) + 1 (x + 1) \\ = (x + 1) (x + 1) \end{matrix}

So, the factored form of the given polynomial expression is

(x + 1) (x + 1)

.
Hence, the correct option is (2).

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

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

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!