con a) mik cứ thấy sai sai nên bn xem lại nhé:

b) 2x3 + x2 - 4x - 12

= 2x3 - 4x2 + 5x2 - 10x + 6x - 12

= (2x3 - 4x2) + (5x2 - 10x) + (6x - 12)

= 2x2(x - 2) + 5x(x - 2) + 6(x - 2)

= (2x2 + 5x + 6)(x - 2)

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

= [(2x2 + 2x) + (3x + 6)](x - 2)

= [2x(x + 2) + 3(x + 2)](x - 2)

= (2x + 3)(x + 2)(x - 2)

= (2x + 3)(x2 - 4)

c) x3 - 9x2 + 14x

= x3 - 7x2 - 2x2 + 14x

= (x3 - 7x2) - (2x2 - 14x)

= x2(x - 7) - 2x(x - 7)

= (x2 - 2x)(x - 7)

= x(x - 2)(x - 7)

d) x5 - xy4 + x4y - y5

= (x5 + x4y) - (xy4 + y5)

= x4(x + y) - y4(x + y)

= (x4 - y4)(x + y)

= (x2 + y2)(x2 - y2)(x + y)

= (x2 + y2)(x - y)(x + y)(x + y)

= (x2 + y2)(x - y)(x + y)2

e) (x + 1)(x + 3)(x + 5)(x + 7) - 9

= [(x + 1)(x + 7)][(x + 3)(x + 5)] - 9

= (x2 + 7x + x + 7)(x2 + 5x + 3x + 15) - 9

= (x2 + 8x + 7)(x2 + 8x + 15) - 9

Thay x2 + 8x + 7 = y, ta có:

y(y + 8) - 9

= y2 + 8y - 9

= y2 - y + 9y - 9

= (y2 - y) + (9y - 9)

= y(y - 1) + 9(y - 1)

= (y + 9)(y - 1)

= (x2 + 8x + 7 + 9)(x2 + 8x + 7 - 1)

= (x2 + 8x + 16)(x2 + 8x + 6)

= (x + 4)2.(x2 + 8x + 6)

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