幾題十字相乘的數(10分)..........

1.6w^2+13w+6
6W可以分拆成1w,6w及2w,3w,
同樣6也可以分拆成1,6及2,3
所以用十字相乘可有以下組合
(w+6)(6w+1)
(w+1)(6w+6)
(w+2)(6w+3)
(w+3)(6w+2)
(2w+2)(3w+3)
(2w+3)(3w+2)
(2w+6)(3w+1)
(2w+1)(3w+6)

根據題目,中間是13x
所以只有(2w+3)(3w+2)符合題目
6w^2+13w+6
=(2w+3)(3w+2)


2-6題分析與第一題一樣,你自己試試
給答案你吧

2.12y^2-17y+6
=(12y-3)(y-2)


3.12m^2+25m+12
=(3m+4)(4m+3)


4.2-15x-8x^2
=(1-8x)(2+x)

5.5x^2-9x-2
=(x-2)(5x+1)

6.-5y^2+12-4y
=(-5y+6)(y+2)

1.
6w^2+13w+6
=6w^2+9w+4w+6
=(6w^2+9w)+(4w+6)
=3w(2w+3)+2(2w+3)
=(2w+3)(3w+2)

2.
12y^2-17y+6
=12y^2+8y+9y+6
=(12y^2+8y)+(9y+6)
=4y(3y+2)+3(3y+2)
=(3y+2)(4y+3)

3.
12m^2+25m+12
=12m^2+16m+9m+12
=(12m^2+16m)+(9m+12)
=4m(3m+4)+3(3m+4)
=(3m+4)(4m+3)

4.
2-15x-8x^2
=2+x-16x-8x^2
=(2+x)-(16x+8x^2)
=(x+2)-8x(x+2)
=(x+2)(1-8x)

5.
5x^2-9x-2
=5x^2-10x+x-2
=(5x^2-10x)+(x-2)
=5x(x-2)+(x-2)
=(x-2)(5x+1)

6.
-5y^2+12-4y
=-5y^2-4y+12
=-5y^2-10y+6y+12
=-(5y^2+10y)+(6y+12)
=-5y(y+2)+6(y+2)
=(y+2)(6-5y)