數學多項式問題

6(a)ab+2b-3a-6
=b(a+2)-3(a+2)
=(a+2)(b-3)

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

7 (a)a2-a-ab+b
=a(a-1)-b(a-1)
=(a-b)(a-1)

(b)a2-b2-a+b
=(a-b)(a+b)-(a-b)
=(a-b)(a+b-1)

12(a)a2-b2-2a+1
=a2-2a+1-b2
=(a-1)2-b2
=[(a-1)-b] [(a-1)+b]
=(a-b-1)(a+b-1)

(b)2ab-a2-b2+c2
=-(a2-2ab+b2)+c2
=-(a-b)2+c2
=c2-(a-b)2
=[c-(a-b)] [c+(a-b)]
=(c-a+b)(c+a-b)

19 (a) x2 + 3x – 18
=(x-3)(x+6)

(b) a2+b2+2ab+3a+3b-18
=(a+b)2+3(a+b)-18
=[(a+b)-3] [(a+b)+6]
=(a+b-3)(a+b+6)

20 (a) 3x2 +13x+ 12
=(3x+1)(x+4)

(b) 3(100)2+13(100)+12
=[3(100)+1](100+4)
=(301)(104)

6(a). ab + 2b - 3a - 6 =a(b+2)-3(a+2)
(b). ab - ad - 2bc + 2cd =a(b-d)-2c(b-d)

7 (a). a^2 -a - ab +b =a(a-1)-b(a-1)
(b). a^2 - b^2 - a +b =(a+b)(a-b)-(a-b)=(a-b)(a+b-1)

12 (a). a^2 - b^2 - 2a +1 =(a+b)(a-b)-(2a-1)
(b). 2ab- a^2 - b^2 + c^2 =2ab-(a+b)(a-b)+c^2

19 (a). 因式分解 x^2 + 3x - 18=(x-3)(x+6)
(b). 利用(a)部的結果,因式分解a^2 + b^2 + 2ab + 3a + 3b - 18
= a^2 + 3a - 18+ b^2 + 2ab + 3b
=(a-3)(a+6)+b(b+2a+3)

20 (a). 因式分解 3x^2 +13x+ 12 =(3x+4)(x-3)
(b). 利用(a) 部的結果,求整數 31 312 的質因數連乘式