### Chapter 2: Polynomials

Q
##### Polynomials CBSE NCERT Solutions

Question:

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

(i) t2 - 3, 2t+ 3t3 - 2t2 - 9t – 12

(ii) x2 + 3x + 1 , 3x4 + 5x3 - 7x2 + 2x + 2

(iii) x3 - 3x + 1, x5 - 4x3 + x2 + 3x + 1

Solutions:

(i) t- 3, 2t+ 3t- 2t- 9t – 12

We have,

The first polynomial is t2 - 3 and the second polynomial is 2t+ 3t3 - 2t- 9t -12. Here, remainder is zero.

Hence, t2 -3 is a factor of 2t2 + 3t+ 4.

(ii) x2 + 3x + 1 , 3x4 + 5x3 - 7x2 + 2x + 2

We have,

First polynomial is x2 + 3x + 1 and Second polynomial is  3x4 + 5x3 - 7x2 + 2x + 2. Here, the remainder is left as 0.

Hence, x2 + 3x + 1 is a factor of 3x4 + 5x3 - 7x2 +2x + 2.

(iii) x3 - 3x + 1, x5 - 4x3 + x2 + 3x + 1

We have,

First polynomial is x3 - 3x + 1 and Second polynomial is x5- 4x3 + x2 + 3x + 1. Hence,  the remainder is not equal to 0.

Hence, x3- 3x + 1 is not a factor of x5- 4x3 + x2 + 3x + 1 .

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