因式分解 x^4+x^3-6x^2-4x+8

解答

因式分解

x^{4} + x^{3} - 6 x^{2} - 4 x + 8

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

求解步骤

x^{4} + x^{3} - 6 x^{2} - 4 x + 8

使用有理根定理

= (x - 1) \frac{x ^{4} + x ^{3} - 6 x ^{2} - 4 x + 8}{x - 1}

\frac{x ^{4} + x ^{3} - 6 x ^{2} - 4 x + 8}{x - 1} = x^{3} + 2 x^{2} - 4 x - 8

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

因式分解

x^{3} + 2 x^{2} - 4 x - 8 : (x + 2) (x + 2) (x - 2)

= (x - 1) (x + 2) (x + 2) (x - 2)

使用指数法则:

aa = a^{2}

(x + 2) (x + 2) = (x + 2)^{2}

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

s im pl i f y (t^{8})^{2}

2 (5 x - 6) = 3 (3 x + 2) + x

5 x - x^{2} = 0

x^{2} + 5^{2} = (52)^{2}

- \frac{1}{4} x + 8 \leq 12