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
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 = 2t4 +3t3-2t2 -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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