Question

若五個(gè)有理數(shù)的積是負(fù)數(shù)，則這五個(gè)有理數(shù)中正因數(shù)的個(gè)數(shù)是（　�。�

A．0個(gè)或2個(gè)

B．1個(gè)或3個(gè)

C．0個(gè)或2個(gè)或4個(gè)

D．1個(gè)或3個(gè)或5個(gè)

Answer 1

分析：根據(jù)有理數(shù)的乘法運(yùn)算符號(hào)法則判斷出負(fù)因數(shù)的個(gè)數(shù)，然后求出正因數(shù)的個(gè)數(shù)即可．

解答：解：∵五個(gè)有理數(shù)的積是負(fù)數(shù)，
∴負(fù)因數(shù)的個(gè)數(shù)是1或3或5個(gè)，
∴正因數(shù)的個(gè)數(shù)為4或2或0個(gè)．
故選C．

點(diǎn)評(píng)：本題考查了有理數(shù)的乘法，熟記幾個(gè)不等于零的數(shù)相乘，積的符號(hào)由負(fù)因數(shù)的個(gè)數(shù)決定：當(dāng)負(fù)因數(shù)有奇數(shù)個(gè)數(shù)，積為負(fù)；當(dāng)負(fù)因數(shù)的個(gè)數(shù)為偶數(shù)個(gè)時(shí)，積為正．