因式分解 36x^4-97x^2+36

解答

因式分解

36 x^{4} - 97 x^{2} + 36

(3 x + 2) (3 x - 2) (2 x + 3) (2 x - 3)

求解步骤

36 x^{4} - 97 x^{2} + 36

令

u = x^{2}

= 36 u^{2} - 97 u + 36

因式分解

36 u^{2} - 97 u + 36 : (9 u - 4) (4 u - 9)

= (9 u - 4) (4 u - 9)

u = x^{2}

代回

= (9 x^{2} - 4) (4 x^{2} - 9)

因式分解

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

= (3 x + 2) (3 x - 2) (4 x^{2} - 9)

因式分解

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

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

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