數學問題因式分解

(a) 6x+18x^2
解：6x+18x^2
=6x(3x+1)

(b) 15xy-5y
解：15xy-5y
=5y(3x-1)

(c) 2bc-10ab+cd+5ad(原題是否錯誤？應該是2bc+10ab+cd+
5ad，因為三正一負不能分組因式分解)
解：2bc+10ab+cd+5ad
=2b(c+5a)+d(c+5a)
=(5a+c)(2b+d)

(d) 36a^2-b^2+6a-6b(原題是否錯誤？應該是36a^2-b^2+6a-b)
解：36a^2-b^2+6a-b
=(6a+b)(6a-b)+(6a-b)
=(6a-b)(6a+b+1)

(e) x^2-144
解：x^2-144
=(x+12)(x-12)

(f) 3x^2-27
解：3x^2-27
=3(x^2-9)
=3(x+3)(x-3)

(g) 5x^2-125
解：5x^2-125
=5(x^2-25)
=5(x+5)(x-5)

(h) x^2-5x+6
解：x^2-5x+6
=(x-2)(x-3)

(i) 2x^2-3x-54
解：2x^2-3x-54
=(x-6)(2x+9)


(j) 4x^2-14x-18)
解：4x^2-14x-18
=2(2x^2-7x-9)
=2(x+1)(2x-9)

６x+18x^2
6x(1+3x)
___________________________
15xy-5y
5y(3x-1)
_____________________________
2bc-10ab+cd+5ad
Can not be factorized
________________________
36a^2-b^2+6a-6b
(6a+b)(6a-b)+6(a-b)
_________________________
x^2-144
(x+12)(x-12)
______________________
3x^2-27
3(x^2-9)
3(x+3)(x-3)
________________________
5x^2-125
5(x^2-25)
5(x+5)(x-5)
_________________________
x^2-5x+6
(x-3)(x-2)
______________________
2x^2-3x-54
(2x+9)(x-6)
___________________
4x^2-14x-18
2(2x^2-7x-9)
(2x-9)(x+1)

(a)6x+18x^2
=6x(3x+1)


(b)15xy-5y
=5y(3x-1)

(c) 這個問題請重睇一次(因這是不能因式分解的)
我猜問題是這的:
2bc-10ab+cd-5ad
=2b(c-5a)+d(c-5a)
=(2b+d) (c-5a)

或者是,

2bc-10ab-cd+5ad
=2b(c-5a)-d(c-5a)
=(2b-d) (c-5a)

(d) 這個問題都請重睇一次(因這是不能因式分解的)
我猜問題是這的:
36a^2-b^2+6a-b
=(6a)^2-b^2+6a-b
=(6a-b) (6a+b) +1 (6a-b)
=(6a-b) [(6a+b)+1]
=(6a-b) (6a+b+1)



(e)x^2-144
=x^2-12^2
=(x-12) (x+12)


(f)3x^2-27
=3(x^2-9)
=3(x^2-3^2)
=3(x-3) (x+3)


(g)5x^2-125
=5(x^2-25)
=5(x^2-5^2)
=5(x-5) (x+5)

(h)x^2-5x+6
=x^2-3x-2x+6
=x(x-3)-2(x-3)
=(x-2) (x-3)

(i)2x^2-3x-54
=2x^2-12x+9x-54
=2x(x-6)+9(x-6)
=(2x=9) (x-6)


(j)4x^2-14x-18
=4x^2+4x-18x-18
=4x(x+1)-18(x+1)
=(4x-18) (x+1)

善用恆等式和注意因子的抽出,這樣有助你做因式分解的問題。


希望我可以幫到你!

(a): 6x+18x^2 = 6x(3x+1)
(b): 15xy-5y = 5y(3x-1)
(c): 2bc-10ab+cd+5ad = c(2b+d) - 5a(2b-d) <--- 你有無打錯題目？
(d): 36a^2 - b^2 + 6a - 6b = (6a+b)(6a-b)+6(a-b) <--- 你有無打錯題目？
(e): x^2-144 = (x+12)(x-12)
(f): 3x^2-27 = 3(x^2 - 9) = 3(x+3)(x-3)
(g): 5x^2-125 =5(x+5)(x-5)
(h): x^2-5x+6 = (x-2)(x-3) <--- 可以按機！
(i): 2x^2-3x-54 = (2x+9)(x-6)
(j): 4x^2-14x-18 = 2(2x-9)(x+1)