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因式分解是一种重要的数学思想方法,这里介绍因式分解在解题中的几种应用.供参考.一、用于整除例1已知296-1可被60至70之间的两个整数整除,这两个数是多少?解296-1=(248+1)(248-1)=…=(248+1)(224+1)(212+1)(26+1)(26-1)=(248+1)(224+1)(212+1)×65×63.∴296-1可被63、65整除.即这两个数是63、65.二、用于计算例2计算:(12+32+…+992)-(22+42+…+1002).
Factorization is an important method of mathematical thinking, here introduced factorization in the problem-solving in a few applications for reference. First, for divisibility example 1 known 296-1 can be 60 to 70 between the two An integral divisibility, what is the sum of these two? Solution 296-1 = (248 + 1) (248-1) = ... = (248 + 1) (224 + 1) (212 + 1) 26-1) = (248 + 1) (224 + 1) (212 + 1) × 65 × 63. The value of 296-1 can be divided by 63 and 65. That is, these two numbers are 63 and 65. Calculation example 2 calculates: (12 + 32 + ... + 992) - (22 + 42 + ... + 1002).