Factorize the polynomial expression $x^{2} + 13 x + 40$ , and choose the option which represents the factored form correctly.

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

(x + 8) (x - 3)

(x - 5) (x - 8)

(x + 5) (x + 8)

(x - 5) (x + 8)

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

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

Take Free Test

Detailed Solution

A polynomial expression

x^{2} + 13 x + 40

is given and it is asked to determine its factors.
To do so, we will have to use the method of middle-term splitting.
To do so, first we need to find the product of the first and last terms of the given polynomial function, i.e.,

x^{2} \times 40 = 40 x^{2}

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

13 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.,

40 x^{2}

x^{2} + 13 x + 40 \Leftrightarrow x^{2} + 5 x + 8 x + 40

Now, we need to group the terms and factor them out, as follows.

\begin{array}{l} (x^{2} + 5 x) + (8 x + 40) \\ x (x + 5) + 8 (x + 5) \\ (x + 5) (x + 8) \end{array}

So, the factored form of the given polynomial expression is

(x + 5) (x + 8)

.
Hence, the correct option is (2).

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!