因式分解 x^4-10x^3+35x^2-50x+24

解答

因式分解

x^{4} - 10 x^{3} + 35 x^{2} - 50 x + 24

(x - 1) (x - 2) (x - 3) (x - 4)

求解步骤

x^{4} - 10 x^{3} + 35 x^{2} - 50 x + 24

使用有理根定理

= (x - 1) \frac{x ^{4} - 10 x ^{3} + 35 x ^{2} - 50 x + 24}{x - 1}

\frac{x ^{4} - 10 x ^{3} + 35 x ^{2} - 50 x + 24}{x - 1} = x^{3} - 9 x^{2} + 26 x - 24

= (x - 1) (x^{3} - 9 x^{2} + 26 x - 24)

因式分解

x^{3} - 9 x^{2} + 26 x - 24 : (x - 2) (x - 3) (x - 4)

= (x - 1) (x - 2) (x - 3) (x - 4)

s im pl i f y \frac{2}{9} \cdot 6

r - 12 = 9 r - 8

s im pl i f y \frac{a ^{2} - b ^{2}}{\frac{ab}{\frac{a - b}{b}}}

s im pl i f y ln (- 37)

- x^{2} - 2 x = 0