1. Find the G.C.D. and L.C.M. of 64x³+1, 16x²+8x+1 and 16x²-1.
2. Find the G.C.D. and L.C.M. of 6x²+7x-3, 3x²+5x-2 and 9x²-6x+1.
3. If the G.C.D. and L.C.M. of (x+2)(x+3)²(2x-1)^4 and Q(x) are (x+2)(x+3) and 3(x+2)³(x+3)²(2x-1)^4 respectively, find Q(x).
Rational Functions(LCM&GCD)
2015-01-31 12:37 am
回答 (1)
2015-01-31 8:38 am
✔ 最佳答案
1.64x³ + 1 = (4x + 1)(16x² -4x + 1)
16x² + 8x + 1 = (4x + 1)²
16x² - 1 = (4x + 1)(4x - 1)
G.C.D. = 4x + 1
L.C.M. = (4x + 1)²(4x - 1)( 16x² -4x + 1)
====
2.
6x² + 7x - 3 = (3x - 1)(2x + 3)
3x² + 5x - 2 = (3x - 1)(x + 2)
9x² - 6x + 1 = (3x - 1)²
G.C.D. = 3x - 1
L.C.M. = (3x - 1)²(2x + 3)(x + 2)
====
3.
Q(x)•(x + 2)(x + 3)²(2x - 1)⁴ = (x + 2)(x + 3)•3(x + 2)³(x + 3)²(2x - 1)⁴
Q(x) = 3(x + 2)³(x + 3)
收錄日期: 2021-04-15 18:04:09
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