Q2 of 108 Page 38

Dividing the first polynomial, by the second polynomial, check whether the first polynomial is a factor of the second polynomial:

g(x) = x2 + 3x + 1, f(x) = 3x4 + 5x3 – 7x2 + 2x + 2


The solution is as follows:


Since the remainder is zero, it is proved that the first polynomial is the factor of second.


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Find the quotient and the remainder on dividing f(x) by using division algorithm.

f(x) = x3 – 6x2 + 11x – 6, g(x) = x + 2


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f(x) = 9x4 – 4x2 + 4, g(x) = 3x2 + x – 1


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Dividing the first polynomial, by the second polynomial, check whether the first polynomial is a factor of the second polynomial:

g(t) = t2 – 3, f(t) = 2t4 + 3t3 – 2t2 – 9t – 12


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Dividing the first polynomial, by the second polynomial, check whether the first polynomial is a factor of the second polynomial:

g(x) = x3 – 3x + 1, f(x) = x5 – 4x3 + x2 + 3x + 1