Question

phân tích đa thức thành nhân tử :

a, \(x^3-x^2-4x^2+8x-4\)

b, \(x^2-2x-4y^2-4y\)

c, \(x^3+10x^2+25x-xy^2\)

d, \(x^3-4x^2+12x-27\)

e, \(x^2+x-6\)

f, \(2x^2+4x-30\)

help !!! cần gấp lắm , bạn nào lm đúng mik tick cho , giúp nhé !

Answer 1

a)

\(x^3-x^2-4x^2+8x-4\)

\(=(x^3-x^2)-(4x^2-8x+4)\)

\(=x^2(x-1)-4(x^2-2x+1)=x^2(x-1)-4(x-1)^2\)

\(=(x-1)[x^2-4(x-1)]=(x-1)(x^2-4x+4)=(x-1)(x^2-2.2x+2^2)\)

\(=(x-1)(x-2)^2\)

b)

\(x^2-2x-4y^2-4y\)

\(=(x^2-2x+1)-(4y^2+4y+1)\)

\(=(x-1)^2-(2y+1)^2=[(x-1)-(2y+1)][(x-1)+(2y+1)]\)

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

Answer 2

c)

\(x^3+10x^2+25x-xy^2\)

\(=x(x^2+10x+25-y^2)\)

\(=x[(x^2+10x+25)-y^2]=x[(x^2+2.5x+5^2)-y^2]=x[(x+5)^2-y^2]\)

\(=x(x+5-y)(x+5+y)\)

d)

\(x^3-4x^2+12x-27=(x^3-27)-(4x^2-12x)\)

\(=(x^3-3^3)-4x(x-3)=(x-3)(x^2+3x+9)-4x(x-3)\)

\(=(x-3)(x^2-x+9)\)

Answer 3

e)

\(x^2+x-6=x^2-2x+3x-6\)

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

f)

\(2x^2+4x-30=2(x^2+2x+1)-32\)

\(=2(x+1)^2-32=2[(x+1)^2-16]=2[(x+1)^2-4^2]\)

\(=2[(x+1-4)(x+1+4)]=2(x-3)(x+5)\)