Question

用余式定理来因式分解：6x^4+5x^3-38x^2+5x+6

Answer 1

6x^4+5x^3-38x^2+5x+6
=(6x^4+5x^3-39x^2)+(x^2+5x+6)
=x^2(6x^2+5x-39)+(x+2)(x+3)
=x^2(x+3)(6x-13)+(x+2)(x+3)
=(x+3)(6x^3-13x^2+x+2)
=(x+3)(6x^3-13x^2+2x-x+2)
=(x+3)[x(6x^2-13x+2)-(x-2)]
=(x+3)[x(x-2)(6x-1)-(x-2)]
=(x+3)[(x-2)(6x^2-x-1)]
=(x+3)(x-2)(2x-1)(3x+1)
或者
6x^4+ 5x³ -38x² + 5x + 6
=6x^4+5x^3-38x^2+5x+6
=6x^4-12x^3+17x^3-34x^2-4x^2+8x-3x+6
=(6x^4-12x^3)+(17x^3-34x^2)-(4x^2-8x)-(3x-6)
=6x^3(x-2)+17x^2(x-2)-4x(x-2)-3(x-2)
=(x-2)(6x^3+17x^2-4x-3)
=(x-2)(6x^3+18x^2-x^2-3x-x-3)
=(x-2)[(6x^3+18x^2)-(x^2+3x)-(x+3)]
=(x-2)[(6x^2(x+3)-x(x+3)-(x+3)]
=(x-2)(x+3)(6x^2-x-1)
=(x-2)(x+3)(2x-1)(3x+1)

Answer 2

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