6x&sup4; + 5x³ -38x² + 5x + 6 因式分解

题目

6x&sup4; + 5x³ -38x² + 5x + 6 因式分解

答案

6x&sup4; + 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)