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On the Independence Day celebration in the school some students participated in the celebration. School management has decided to distribute some sweets amongst the participants and the audience. If total number of sweets were represented by $8 x 4 + 14 x 3 − 2 x 3 + 7 x − 8$ and each one received $2 x 2 + 2 x − 1$ sweets and $14 x − 10$ remained undistributed. Find the number of students to whom sweets were distributed.

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4 x 2 + 3 x − 2

2 x 2 − 5 x − 20

2 x 2 + 5 x + 20

4 x 2 − 3 x + 2

answer is A.

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Detailed Solution

Given polynomial

8 x 4 + 14 x 3 − 2 x 3 + 7 x − 8

represents the total number of sweets and each student received

2 x 2 + 2 x − 1

sweets.
Remaining sweets are represented by

14 x − 10

.
We need to find the number of students to whom sweets were distributed.
By division algorithm, we have,

D i v i d e n d = Q u o t i e n t × D i v i s o r + R e m a i n d e r .

From the question we have,
Dividend

= 8 x 4 + 14 x 3 − 2 x 3 + 7 x − 8

Quotient

= 2 x 2 + 2 x − 1

Remainder

= 14 x − 10

Let us assume the number of students to whom sweets were distributed are

z

and this

z

will work as our divisor.
Therefore, equating all these values in division algorithm, we have,

⇒ 8 x 4 + 14 x 3 − 2 x 2 + 7 x − 8 = 2 x 2 + 2 x − 1 × z + (14 x − 10)

⇒ 8 x 4 + 14 x 3 − 2 x 2 + 7 x − 14 x − 8 + 10 = 2 x 2 + 2 x − 1 × z

⇒ 8 x 4 + 14 x 3 − 2 x 2 − 7 x + 2 = 2 x 2 + 2 x − 1 × z

⇒ z = 8 x 4 + 14 x 3 − 2 x 2 − 7 x + 2 2 x 2 + 2 x − 1

Now, dividing

8 x 4 + 14 x 3 − 2 x 2 − 7 x + 2

2 x 2 + 2 x − 1

we have,

Hence, the number of students to whom the sweets were distributed are

4 x 2 + 3 x − 2

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