Question 1:
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
(i) p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 – 2
(ii) p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 – x
(iii) p(x) = x4 – 5x + 6, g(x) = 2 – x2
Answer:
Quotient = x − 3
Remainder = 7x − 9
p(x) = x4 – 3x2 + 4x + 5 = x4 + 0.x3 – 3x2 + 4x + 5
q(x) = x2 + 1 – x = x2 – x + 1
Quotient = x2 + x − 3
Remainder = 8
(iii) p(x) = x4 – 5x + 6 = x4 + 0.x2 – 5x + 6
q(x) = 2 – x2 = – x2 + 2
Quotient = −x2 − 2
Remainder = −5x +10
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