a, x²-6x+5
= x² - x - 5x + 5
= (x² - x) - (5x - 5)
= x(x-1) - 5(x - 1)
= (x-1)(x-5)
b, x²-x-12
= x² + 3x - 4x - 12
= x(x+3) - 4(x+3)
= (x+3)(x-4)
c, x²+8x+15
= x² + 3x + 5x +15
= x(x+3) + 5(x+3)
=(x+3)(x+5)
d,x²+2xy+y²+2x+2y-15
= (x²+2xy+y²)+(2x+2y)-15
= (x+y)² + 2(x+y) - 15
= (x+y)² - 3(x+y) + 5(x+y) - 15
= (x+y)(x+y-3) + 5(x+y-3)
= (x+y-3)(x+y+5)
e, x² +2xy+y²-x-y-12
= (x² +2xy+y²)-(x+y)-12
= (x+y)² - (x+y) - 12
= (x+y)² + 3(x+y) - 4(x+y) - 12
= (x+y)(x+y+3) - 4(x+y+3)
=(x+y+3)(x+y-4)
g, 3x²+13x-10
= 3x² + 15x - 2x - 10
= 3x(x+5) - 2(x+5)
= (x+5)(3x-2)
f, 64x^4+y^4
= 64x^4 + 16x²y² - 16x²y² + y^4
= (64x^4 + 16x²y² + y^4) - 16x²y²
= (8x² + y²)² - (4xy)²
= (8x²+y²-4xy)(8x²+y²+4xy)
i, 2x²-5x-12
= 2x² - 8x + 3x - 12
= 2x(x-4) + 3(x-4)
= (x-4)(2x+3)
