Q1 of 108 Page 38

Find the quotient and the remainder on dividing f(x) by using division algorithm.
f(x) = 9x⁴ – 4x² + 4, g(x) = 3x² + x – 1

The solution is as follows:

Quotient = 3x² – x

Remainder = -x + 4

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

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

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

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

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

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

Questions · 108

3. Polynomials

1 1 1 1 1 1 2 2 2 2 2 2 3 1 1 1 1 2 2 2 3 3 3 4 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 3 4 5 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 4 5 1 1 1 1 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 19 19 19 20 21 21 22 23

Find the quotient and the remainder on dividing f(x) by using division algorithm.f(x) = 9x4 – 4x2 + 4, g(x) = 3x2 + x – 1