因式分解 x^4+7x^2-144

解答

因式分解

x^{4} + 7 x^{2} - 144

(x + 3) (x - 3) (x^{2} + 16)

求解步骤

x^{4} + 7 x^{2} - 144

令

u = x^{2}

= u^{2} + 7 u - 144

因式分解

u^{2} + 7 u - 144 : (u - 9) (u + 16)

= (u - 9) (u + 16)

u = x^{2}

代回

= (x^{2} - 9) (x^{2} + 16)

因式分解

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

= (x + 3) (x - 3) (x^{2} + 16)