Question

Phân tích các đa thức sau thành nhân tử

a) \(12x^3+4x^2-27x-9\)

b) \(x^6-x^4+2x^3+2x^2\)

c) \(30ax-34bx-15a+17b\)

d) \(x^3-x^2y-x^2z-xyz\)

Answer 1

c)

\(30ax-34bx-15a+17b\)

\(=(30ax-15a)-(34bx-17b)\)

\(=15a(2x-1)-17b(2x-1)\)

\(=(2x-1)(15a-17b)\)

d)

\(x^3-x^2y-x^2z-xyz\)

\(=x[x^2-xy-xz-yz]\)

Answer 2

a)

\(12x^3+4x^2-27x-9\)

\(=(12x^3+4x^2)-(27x+9)\)

\(=4x^2(3x+1)-9(3x+1)\)

\(=(3x+1)(4x^2-9)=(3x+1)[(2x)^2-3^2]\)

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

b)

\(x^6-x^4+2x^3+2x^2\)

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

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

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

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

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

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

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

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