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例1分解因式:x~5+x+1.分析∵x~5=x~4·x或x~5=x~3·x~2,如果能分解成一次因式,那么一次因式应是(x-1)或(x+1).而f(1)=3≠0.f(-1)=-1≠0,因此,原式不可能分解成一次因式和四次因式的乘积,只能分解成二次因式和三次因式的乘积.
Example 1 factorization factor: x~5+x+1. Analysis ∵x~5=x~4·x or x~5=x~3·x~2. If it can be decomposed into one factor, then one factor It should be (x-1) or (x+1). And f(1)=3≠0.f(-1)=-1≠0. Therefore, the original formula cannot be decomposed into one factor and four factors. The product of the formula can only be decomposed into the product of the second factor and the cubic factor.