Question

Bài 4

a)\(x^3+6x^2+11x+6\)

b)\(x^3+6x^2-13x-42\)

c)\(x^3-5x^2+8x-4\)

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

Answer 1

a)

\(x^3+6x^2+11x+6=(x^3-x)+(6x^2+12x+6)\)

\(=x(x^2-1)+5(x^2+2x+1)\)

\(=x(x-1)(x+1)+6(x+1)^2\)

\(=(x+1)[x(x-1)+6(x+1)]=(x+1)(x^2+5x+6)\)

\(=(x+1)(x^2+2x+3x+6)\)

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

b) \(x^3+6x^2-13x-42\)

\(=x^3+2x^2+4x^2+8x-21x-42\)

\(=x^2(x+2)+4x(x+2)-21(x+2)\)

\(=(x+2)(x^2+4x-21)\)

\(=(x+2)[x^2-3x+7x-21)\)

\(=(x+2)(x+7)(x-3)\)

Answer 2

c)

\(x^3-5x^2+8x-4=(x^3-x^2)-4x^2+8x-4\)

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

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

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

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

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

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

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

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

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

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

\(=(x+1)(2x^2-3x+6)\)