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Question
Find the quotient and remainder for the following using synthetic division:
(8x4 – 2x2 + 6x + 5) ÷ (4x + 1)
Solution
p(x) = 8x4 – 2x2 + 6x + 5
d(x) = 4x + 1
`-2 + 1/2 = (-4 + 1)/2 = (-3)/2`
`6 + 3/8 = (48 + 3)/8 = 51/8`
`5 - 51/32 = (160 - 51)/32 = 109/32`
The quotient = `1/4(8x^3 - 2x^2 - (3x)/2 + 51/8)`
= `2x^3 - x^2/2 - (3x)/8 + 51/32`
Remainder = `109/32`
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