Question

1.Phân tích đa thức thành nhân tử.

a. x³+5x²+3x-9

b. x³+9x²+11x-21

c. x³-7x+6

d. x³-5x²+8x-4

e. x³-3x+2

f. x³+8x²+17x+10

g. x³+3x²+6x+4

h. x³-2x-4

k. x³+x²+4

l. x³-12x+7x-2

Answer 1

a. x³+5x²+3x-9

= x³-x²+6x²-6x+9x-9

= x²(x-1)+6x(x-1)+9(x-1)

= (x²+6x+9)(x-1)

= (x+3)²(x-1)

b. x³+9x²+11x-21

= x³-x²+10x²-10x+21x-21

= x²(x-1)+10x(x-1)+21(x-1)

= (x²+10x+21)(x-1)

= (x+7)(x+3)(x-1)

c. x³-7x+6

= x³-x²+x²-x-6x+6

= x²(x-1)+x(x-1)-6(x-1)

= (x²+x-6)(x-1)

= (x+3)(x-2)(x-1)

d. x³-5x²+8x-4

= x³-x²-4x²+4x+4x-4

= x²(x-1)-4x(x-1)+4(x-1)

= (x²-4x+4)(x-1)

= (x-2)²(x-1)

e. x³-3x+2

= x³+2x²-2x²-4x+x+2

= x²(x+2)-2x(x+2)+(x+2)

= (x²-2x+1)(x+2)

= (x-1)²(x+2)

f. x³+8x²+17x+10

= x³+5x²+3x²+15x+2x+10

= x²(x+5)+3x(x+5)+2(x+5)

= (x²+3x+2)(x+5)

= (x+1)(x+2)(x+5)

g. x³+3x²+6x+4

= x³+x²+2x²+2x+4x+4

= x²(x+1)+2x(x+1)+4(x+1)

= (x²+2x+4)(x+1)

h. x³-2x-4

= x³-2x²+2x²-4x+2x-4

= x²(x-2)+2x(x-2)+2(x-2)

= (x²+2x+2)(x-2)

k. x³+x²+4

= x³+2x²-x²-2x+2x+4

= x²(x+2)-x(x+2)+2(x+2)

= (x²-x+2)(x+2)

l. x³-12x+7x-2

= x³+2x²-2x²-4x-x-2

= x²(x+2)-2x(x+2)-(x+2)

= (x²-2x-1)(x+2)