(1) Given the following fraction, divide the denominator into the numerator using long division. Give the quotient and the remainder.
(a) 7y2 + 2y - 63
_____________
y + 3
(b) 6x3 - 5x2 + 15x + 5
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2x2 - x + 3
(c) x6 + a6
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x4 - a2x2 + a4
SOLUTION:
(a) 7y - 19
_______________
y + 3 / 7y2 + 2y - 63
7y2 + 21y
---------
-19y - 63
-19y - 57
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-6
= 7y - 19 remainder -6
(b) 3x - 1
_____________________
2x2 - x + 3 / 6x3 - 5x2 + 15x + 5
6x3 - 3x2 + 9x
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- 2x2 + 6x + 5
- 2x2 + x - 3
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5x + 8
= 3x - 1 remainder 5x + 8
(c) x2 + a2
______________________
x4 - a2x2 + a4 / x6 + a6
x6 - a2x4 + a4x2
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a2x4 - a4x2 + a6
a2x4 - a4x2 + a6
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0
= x2 + a2 (remainder 0)