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因式分解的拆添项技巧一般较难掌握。对于一个多项式f(x),当已知它有一零点a,即有f(x)=0时,依据因式定理,f(x)便有一个一次因式(x-a),这时对f(x)因式分解之拆添项便有章可循:可按系数比1:-a进行拆、添,下面举几例以示其法。 例1 分解因式:x~3+x~2-x-10. 析解 因为整系数多项式f(x)的最高项系数为1时,a是其常数项-10的约数,有±1,±2、±5,
Decomposition-deconstruction techniques are generally more difficult to master. For a polynomial f(x), when it is known that it has a zero a, ie, f(x)=0, according to the factor theorem, f(x) has a one-time factor (xa), which is then f(x). x) Decomposition of items by factorization: There is a rule that can be decomposed and added by a coefficient ratio of 1: -a. Here are some examples to illustrate the method. Example 1 factorization factor: x~3+x~2-x-10. Analysis Since the highest-term coefficient of the integer polynomial f(x) is 1, a is a divisor whose constant term is -10, with ±1. , ±2, ±5,