x^4+x^2-20
= x^4+5x²- 4x²-20
= x²(x²+5)- 4(x²+5)
= (x²+5)(x²-4)
(x²+x)²+4(x²+x)-12
= (x²+x)²+6(x²+x)- 2(x²+x)-12
= (x²+x)(x²+x+6)- 2(x²+x+6)
= (x²+x+6)(x²+x-2)
(x²+x)²+ 9x²+9x+14
=(x²+x)²+ 9(x²+x)+14
=(x²+x)²+ 7(x²+x)+ 2(x²+x)+14
= (x²+x)(x²+x+7)+ 2(x²+x+7)
= (x²+x+7)(x²+x+2)
(x-y)²+4x-4y-12
= (x-y)²+4(x-y)-12
= (x-y)²+ 6(x-y)- 2(x-y)-12
= (x-y+6)(x-y)- 2(x-y+6)
= (x-y+6)(x-y-2)
(x²+x)²-2(x²+x)-15
= (x²+x)²- 5(x²+x)+3(x²+x)-15
= (x²+x)(x²+x-5)+3(x²+x-5)
= (x²+x-5)(x²+x+3)
(x²-x)²+3(x²-x)+2
= (x²-x)²+2(x²-x)+ (x²-x)+2
= (x²-x)(x²-x+2)+ (x²-x+2)
= (x²-x+2)(x²-x+1)
(x²+3x)²+7x²+21x+12
= (x²+3x)²+7(x²+3x)+12
= (x²+3x)²+3(x²+3x)+4(x²+3x)+12
= (x²+3x)(x²+3x+3)+ 4(x²+3x+3)
= (x²+3x+3)(x²+3x+4)
