Question 2

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
(i) t2 – 3, 2t4 + 3t3 – 2t2 – 9t – 12

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

(iii) x3 – 3x + 1, x5 – 4x3 + x2 + 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 = t2-3

                     Second polynomial =  2t+3t3-2t-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 = x2+3x+1

   Second polynomial = 3x4 + 5x3 – 7x2 + 2x + 2

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