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今天是
90天數學指考計畫
DAY10
題目:多項式的運算
f (x)﹐g (x)均為n次多項式﹐且h(x) = g (x) - f (x)﹐則h(x)可能為
(1)零多項式
(2)零次多項式
(3)n次多項式
(4)(n - 1)次多項式
(5)(n + 1)次多項式﹒
解答
(1)(2)(3)(4)
解析
(1)例﹕g (x) = x2 + 1﹐f (x) = x2 + 1﹐
g (x) - f (x) = 0﹒
(2)例﹕g (x) = x2 + 1﹐f (x) = x2 - 1﹐
g (x) - f (x) = 2 ¹ 0﹒
(3)例﹕g (x) = x2 + 1﹐f (x) = x﹐
g (x) - f (x) = x2 - x + 1﹒
(4)例﹕g (x) = x2 + 1﹐f (x) = x2 - x + 2﹐
g (x) - f (x) = x - 1﹒
故選(1)(2)(3)(4)
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