數學之因式分解~20點

Question

請幫我解以下ㄉ題目(需附上計算過程)
1.因式分解-5x(x-2)-3(2-x) x=?

2.若(-x-1)的二次-5x-5可因式分解為(x+1)(ax+b)，則a的二次+b=?

3.因式分解(x-7)的7次方-(7-x)的8次方=?

4.因式分解(x-2)的3次方+(2-x)(x+2)(x+3)=?

5.計算328*0.64-9*1.28+328*0.36-9*0.72=

6.因式分解xy+1-y-x

7.因式分解6-2b-3a+ab=

Answer 1

1.因式分解-5x(x-2)-3(2-x) x=?
解: -5x(x-2)-3(2-x) x
=-5x(x-2)+3(x-2) x …….-(2-x)=(x-2)
=(x-2)(-5x+3x)…………..提公因式
=-2x(x-2) 答: -2x(x-2)

2.若(-x-1)的二次-5x-5可因式分解為(x+1)(ax+b)，則a的二次+b=?
解: (-x-1)的二次-5x-5=(x+1)(ax+b)
X2+2x+1-5x-5=ax2+ax+bx+b……各自展開
X2-3x-4=ax2+(a+b)x+b………….各自合併
故a=1，b=-4，
a的二次+b=1-4=-3 答:-3

3.因式分解(x-7)的7次方-(7-x)的8次方=?
解: (x-7)的7次方-(7-x)的8次方
=(x-7)7-(x-7)8…….. (7-x)8=(x-7)8
=(x-7)7[1-(x-7)]….. ..提公因式
= (x-7)7 (8-x) 答: (x-7)7 (8-x)

4.因式分解(x-2)的3次方+(2-x)(x+2)(x+3)=?
解: (x-2)的3次方+(2-x)(x+2)(x+3)
=(x-2)3-(x-2) (x+2)(x+3)…….. (2-x)=- (x-2)
=(x-2)[ (x-2)2-(x+2)(x+3)] ……提公因式
=(x-2)( -9x-2)………………....展開，再合併
= -(x-2)(9x+2) 答: -(x-2)(9x+2)

5.計算328*0.64-9*1.28+328*0.36-9*0.72=
解: 328*0.64-9*1.28+328*0.36-9*0.72
=(328*0.64+328*0.36)-(9*1.28+9*0.72)…..分組
=328*(0.64+0.36)-9*(1.28+0.72)…………各提公因數
=328-9*2
=310 答:310

6.因式分解xy+1-y-x
解: (xy-x) –(y-1)…….分組
=x(y-1) –(y-1)……….提公因式x
=(y-1)(x-1) 答: (y-1)(x-1)

7.因式分解6-2b -3a +ab=
解: (6-2b)-( 3a -ab) …….分組
=2(3-b)-a(3-b) ……….提公因式
=(3-b)(2-a) 答: (3-b)(2-a)

Answer 2

1. 原式=(x-2)(-5x+3x)=(x-2)(-2x)=-2x(x-2)
2. (-x-1)^2-5x-5=x^2+2x+1-5x-5=x^2-3x-4=(x-4)(x+1) (利用十字交乘)
所以 a=1, b=-4, a^2+b=1-4=-3
3. (x-7)^7-(7-x)^8=(x-7)^7-(x-7)^8=[(x-7)^7][1-(x-7)]=(x-7)^7(8-x)=-(x-7)^7(x-8)
4. (x-2)^3+(2-x)(x+2)(x+3)=(x-2)[(x-2)^2-(x+2)(x+3)=(x-2)(x^2-4x+4-x^2-5x-6)
=(x-2)(-9x-2)=-(x-2)(9x+2)
5. 原式=328*(0.64+0.36)-9*(1.28+0.72)=328*1-9*2=328-18=310
6. 原式=x(y-1)-(y-1)=(y-1)(x-1)
7. 原式=a(b-3)-2(b-3)=(b-3)(a-2)