Question

帮忙分解因式（1）12x² +14x-10 (2)6(x-y)² +5(y-x)+1 (3)x² -(m+n)x+mn (4)2a^4-3a^2-14(

(5)4（a+b)^4-13(a+b)^2+9 (6)(2x^2-3x-1)^2+(2x^2-3x-1)-2

Answer 1

（1）12x² +14x-10
=2(6x²+7x-5)
=2(3x+5)(2x-1)

(2)6(x-y)² +5(y-x)+1
=6(x-y)² -5(x-y)+1
=(3x-3y-1)(2x-2y-1)

(3)x² -(m+n)x+mn
=(x-m)(x-n)

(4)2a^4-3a^2-14
=(2a²-7)(a²+2)
=(√2a+√7)(√2a-√7)(a²+2）

(5)4（a+b)^4-13(a+b)^2+9
=[4(a+b)²-9][(a+b)²-1]
=(2a+2b+3)(2a+2b-3)(a+b+1)(a+b-1)

(6)(2x^2-3x-1)^2+(2x^2-3x-1)-2
=(2x²-3x-1+2)(2x²-3x-1-1)
=(2x²-3x+1)(2x²-3x-2)
=(2x-1)(x-1)(2x+1)(x-2)