Question 2

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

(i) t^{2} – 3, 2t^{4} + 3t^{3} – 2t^{2} – 9t – 12

(ii) x^{2} + 3x + 1, 3x^{4} + 5x^{3} – 7x^{2} + 2x + 2

(iii) x^{3} – 3x + 1, x^{5} – 4x^{3} + x^{2} + 3x + 1

Answer

**Note: If on dividing the second polynomial by first we get zero remainder then we say that first Is factor of second polynomial. **

(i) Given ,

First polynomial = t^{2}-3

Second polynomial = 2t^{4 }+3t^{3}-2t^{2 }-9t-12

As we can see the remainder is 0. Thereofre we can say that first polynomial is a factor of second polynomial.

(ii) Given,

First polynomial = x^{2}+3x+1

Second polynomial = 3x^{4 }+ 5x^{3 – }7x^{2 }+ 2x + 2

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