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已知兩個一元二次多項式能因式分解。問該兩個多項式的和能夠因式分解?

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  • 1 decade ago
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    可以

    兩個平方之和或兩個平方之差

    a2-b2=(a+b)(a-b)

    a2+b2=(a+bi)(a-bi)

    根據以上兩條恆等式,如原式符合以上條件,即可運用代用法直接分解。例如,4x+49 就

    可被分解為(2sqrt(x)+7i)(2sqrt(x)+7i)。

    兩個n次方數之差

    an − bn = (a − b)(an − 1 + an − 2b + ...... + bn − 1)

    兩個奇數次方數之和

    an + bn = (a + b)(an − 1 − an − 2b + ...... + ( − 1)n − 1bn − 1)

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