Question

分解因式：4x^4+8x^3-x^2-8x-3

Answer 1

4x^4+8x^3-x^2-8x-3
=4x^4+8x^3+4x^2-(5x^2+5x)-(3x+3)
=4x^2(x^2+2x+1)-5x(x+1)-3(x+1)
=4x^2(x+1)^2-5x(x+1)-3(x+1)
=(x+1)(4x^3+4x^2-5x-3)
=(x+1)(4x^3+4x^2-8x+3x-3)
=(x+1)[4x(x^2+x-2)+3(x-1)]
=(x+1)[4x(x+2)(x-1)+3(x-1)]
=(x+1)(x-1)(4x^2+8x+3)
=(x+1)(x-1)(2x+1)(2x+3)

Answer 2

4x^4+8x^3-x^2-8x-3
=4x^4-4x^3+12x^3-12x^2+11x^2-11x+3x-3
=4x^3(x-1)+12x^2(x-1)+11x(x-1)+3(x-1)
=(x-1)(4x^3+12x^2+11x+3)
=(x-1)(4x^3+4x^2+8x^2+8x+3x+3)
=(x-1)((4x^2(x+1)+8x(x+1)+3(x+1))
=(x-1)(x+1)(4x^2+8x+3)
=(x-1)(x+1)(2x+1)(2x+3)

Answer 3

4x^4-4x^3+12x^3-12x^2+11x-11x+3x-3
=(x-1)(4x^3+4x^2+8x^2+8x+3x+3)
=(x-1)(x+1)(4x^2+8x+3)
=（X-1)(X+1)(2X+3)(2X+1)

Answer 4

4x^4+8x^3-x^2-8x-3
=(x-1)(4x^3+12x^2+11x+3)
=(x-1)(x+1)(4x^2+8x+3)
=(x-1)(x+1)(2x+1)(2x+3)

Answer 5

4x^4+8x^3-x^2-8x-3
=(4x^4-x^2-3)+(8x^3-8x)
=(4x^2+3)(x^2-1)+8(x^2-1)
=(x^2-1)(4x^2+3+8)
=(x+1)(x-1)(4x^2+3x+8)