Q1 of 44 Page 70

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 - x

p(x) = x4 – 3x2 + 4x + 5

g(x) = x2 + 1 – x

On dividing them,



The quotient is x2 – 1 – x

And,

The remainder is 4x + 4

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Verify that 1, -1 and -3 are the zeroes of the cubic polynomial x3 + 3x2 – x - 3 and check the relationship between zeroes and the coefficients.

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Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 - 2

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Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

p(x) = x4 – 5x + 6, g(x) = 2 - x2

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Check in which case the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

t2 – 3, 2t4 + 3t3 – 2t2 – 9t - 12