因式分解 x^4-2x^3+5x^2-8x+4

解答

因式分解

x^{4} - 2 x^{3} + 5 x^{2} - 8 x + 4

(x - 1)^{2} (x^{2} + 4)

求解步骤

x^{4} - 2 x^{3} + 5 x^{2} - 8 x + 4

使用有理根定理

= (x - 1) \frac{x ^{4} - 2 x ^{3} + 5 x ^{2} - 8 x + 4}{x - 1}

\frac{x ^{4} - 2 x ^{3} + 5 x ^{2} - 8 x + 4}{x - 1} = x^{3} - x^{2} + 4 x - 4

= (x - 1) (x^{3} - x^{2} + 4 x - 4)

因式分解

x^{3} - x^{2} + 4 x - 4 : (x - 1) (x^{2} + 4)

= (x - 1) (x - 1) (x^{2} + 4)

使用指数法则:

aa = a^{2}

(x - 1) (x - 1) = (x - 1)^{2}

= (x - 1)^{2} (x^{2} + 4)

s im pl i f y \frac{1}{n !} + \frac{1}{( n + 1 ) !}

s im pl i f y (\frac{3}{7})^{4}

4 = 5 d - 11

f a c t or 7 x^{2} + 35 x + 42

∣ x + 7 ∣ \leq 5