Question

a)4x²-3x-1

b)6x²-11x²

c)x²-7xy+12y²

d)x²-2xy+y²+3x-3y

e)2x²-12x²+17x-2

f)x³-3x+2

g)x³+3x²

h)x³+9x²+26x+24

Answer 1

e) Sửa đề:

$2x^3-12x^2+17x-2=2x^3-4x^2-8x^2+16x+x-2$

$=2x^2(x-2)-8x(x-2)+(x-2)=(x-2)(2x^2-8x+1)$

f)

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

$=(x-1)(x^2+x-2)=(x-1)(x^2-x+2x-2)=(x-1)[x(x-1)+2(x-1)]$

$=(x-1)(x-1)(x+2)=(x-1)^2(x+2)$

g)
$x^3+3x^2=x^2(x+3)$

h)

$x^3+9x^2+26x+24=(x^3+9x^2+27x+27)-x-3$

$=(x+3)^3-(x+3)=(x+3)[(x+3)^2-1]=(x+3)(x+3-1)(x+3+1)$

$=(x+3)(x+2)(x+4)$

Answer 2

a)

$4x^2-3x-1=4x^2-4x+x-1=4x(x-1)+(x-1)=(4x+1)(x-1)$

b)

$6x^2-11x^2=-5x^2$

c)

\(x^2-7xy+12y^2=x^2-4xy-3xy+12y^2\)

\(=x(x-4y)-3y(x-4y)=(x-3y)(x-4y)\)

d)

\(x^2-2xy+y^2+3x-3y=(x^2-2xy+y^2)+(3x-3y)\)

\(=(x-y)^2+3(x-y)=(x-y)(x-y+3)\)