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 – 5x + 6, g(x) = 2 - x²

p(x) = x⁴ – 5x + 6

_{g(x) = 2 – x}²

On dividing them,

The quotient is –x² – 2

And,

The remainder is -5x + 10

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

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

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

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

x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

Questions · 44

3. Polynomials

1 2 3 4 5 1 2 2 2 2 3 3 3 3 3 4 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 4 1 1 1 2 2 2 3 4 5 5 5

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