1. 因式分解 x^2+ 14x+ 49
2. 因式分解 x^2+ 14x+ 49 - xy-7y
3. 設 f(x) = x^3 - 3x^2 - 4x +12
(a) 證明x-3是f(x)的因式。
(b)將 f(x) 因式分解。
因式分解數條
2013-02-11 7:36 am
回答 (2)
2013-02-11 8:12 am
✔ 最佳答案
1.x² + 14x + 49
= (x)² + 2(x)(7) + (7)²
= (x + 7)²
2.
x² + 14x + 49 - xy - 7y
= (x² + 14x + 49) - (xy + 7y)
= (x + 7)² - y(x + 7)
= [(x + 7) - y] (x + 7)
= (x -y + 7)(x + 7)
3.
(a)
f(x) = x³ - 3x² - 4x + 12
f(3) = (3)³ - 3(3)² - 4(3) + 12 = 0
故此，(x - 3) 是 f(x) 的因式。
(b)
f(x)
= x³ - 3x² - 4x + 12
= (x³ - 3x²) - (4x - 12)
= x²(x - 3) - 4(x - 3)
= (x² - 4)(x - 3)
= (x² - 2²)(x - 3)
= (x + 2)(x - 2)(x - 3)
參考: fooks
2013-02-13 8:26 pm
1
x^2+ 14x+ 49
=(x+7)^2
2.
x^2+ 14x+ 49 - xy-7y
=(x+7)^2-y(x+7)
=(x+7)(x-y+7)
3a
f(x) = x^3 - 3x^2 - 4x +12
f(3)=3^3-3(3)^2-4(3)+12
f(3)=0
所以x-3 是f(x)的因式
3b
f(x) = x^3 - 3x^2 - 4x +12
f(x)=(x-3)(x^2-4)
f(x)=(x-3)(x-2)(x+2)
x^2+ 14x+ 49
=(x+7)^2
2.
x^2+ 14x+ 49 - xy-7y
=(x+7)^2-y(x+7)
=(x+7)(x-y+7)
3a
f(x) = x^3 - 3x^2 - 4x +12
f(3)=3^3-3(3)^2-4(3)+12
f(3)=0
所以x-3 是f(x)的因式
3b
f(x) = x^3 - 3x^2 - 4x +12
f(x)=(x-3)(x^2-4)
f(x)=(x-3)(x-2)(x+2)
收錄日期: 2021-04-13 19:17:27
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130210000051KK00227