國中二年級的數學問題

1.x^2+14x+45=(x+9)(x+5)
2.x^2+15x+56=(x+7)(x+8)
3.x^2+3x-28=(x+7)(x-4)
4.x^2-16x-36=(x-18)(x+2)
5.(x+1)^2-3(x+1)-4=(x+1-4)(x+1+1)=(x-3)(x+2)
6.(x-2)^2+(x-2)-6=(x-2+3)(x-2-2)=(x+1)(x-4)
7.6(x-y)^2-13(x-y)+5=(2(x-y)-1)(3(x-y)-5)=(2x-2y-1)(3x-3y-5)
8.6(x-y)^2+11(y-x)+3=6(x-y)^2-11(x-y)+3=(2(x-y)-3)(3(x-y)-1)=(2x-2y-3)(3x-3y-1)
9.5(x-y)^2-13(x-y)-6=(5(x-y)+2)((x-y)-3)=(5x-5y+2)(x-y-3)

1. (x+9)(x+5)
2. (x-8)(x-7)
3. (x-4)(x+7)
4. (x-18)(x+2)
5. [(x+1)-4][(x+1)+1]=(x-3)(x+2)
6. [(x-2)-2] [(x-2)+3]=(x-4)(x+1)
7. [2(x-y)-1][3(x-y)-5]=(2x-2y-1)(3x-3y-5)
8. 6﹝x-y﹞² +11﹝y-x﹞+3 將(y-x)改成(x-y) 但前面+號變-號
=6﹝x-y﹞² -11﹝x-y﹞+3=[2(x-y)-3][3(x-y)-1]
=(2x-2y-3)(3x-3y-1)

9. [5(x-y)+2][(x-y)-3]=(5x-5y+2)(x-y-3)

x²+14x+45 = (x+9)(x+5)

x²-15x+56 = (x-8)(x-7)

x²+3x-28 = (x+7)(x-4)

x²-16x-36 = (x-18)(x+2)

(x+1)² -3﹝x+1﹞- 4 = x²+2x+1-3x-3 = x²-x-2 = (x-2)(x+1)

(x-2)² +﹝x-2﹞ - 6 = x²- 4x+4+x-2 = x²- 3x+2 = (x-2)(x-1)

6﹝x-y﹞² -13﹝x-y﹞+ 5
使 w=x-y
6﹝x-y﹞² -13﹝x-y﹞+ 5 = 6w²-13w+5 = (2w-1)(3w-5)
=(2x-2y-1)(3x-3y-5)

6﹝x-y﹞² +11﹝y-x﹞+3 = 6﹝x-y﹞² - 11﹝x-y﹞+3
注意由 +11﹝y-x﹞ 改為 - 11﹝x-y﹞
使 w=x-y
= 6w²-11w+3 = (2w-3)(3w-1) = (2x-2y-3)(3x-3y-1)


5﹝x-y﹞² - 13﹝x-y﹞- 6 = 5w²-13w-6 = (5w+2)(w-3)
= (5x-5y+2)(x-y-3)

1.(x+9)(x+5)
2.(x-8)(x-7)
3.(x+7)(x-4)
4.(x+2)(x-18)

5.令(x+1)=y.............(y-4)(y+1)
=(x+1-4)(x+1+1)
=(x-3)(x+2)
6.跟5作法一樣
7.令x-y=z....................6z^-13z+5
3 -5
2 -1
=(3z-5)(2z-1)
=(3x-3y-5)(2x-2y-1)

8. 6(x-y)^+11(y-x)+3
=6(x-y)^-11(-y+x)+3
=6(x-y)^-11(x-y)+3..............剩下跟7一樣

9.跟7一樣