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Question
If the quotient obtained on dividing (8x4 – 2x2 + 6x – 7) by (2x + 1) is (4x3 + px2 – qx + 3), then find p, q and also the remainder
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Solution
p(x) = 8x4 – 2x2 + 6x – 7
d(x) = 2x + 1
2x + 1 = 0
2x = – 1
x = `-1/2`
The quotient = `1/2` [8x3 – 4x2 + 6]
= 4x3 – 2x2 + 3
= 4x3 – 2x2 + 0x + 3
The given quotient is = 4x3 + px2 – qx + 3 .........(compared with the given quotient)
The value of p = – 2 and q = 0
Remainder = – 10
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