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सिद्ध कीजिए कि (x – 1), बहुपद x10 – 1 तथा x11 – 1 का गुणनखण्ड है।

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(x – 1), बहुपद x10 – 1 का गुणनखण्ड होगा। यदि x – 1 = 0 या x = 1 रखने पर

x10 – 1 का शेषफल = (1)10 – 1 = 1 – 1 = 0

∴ (x – 1), x10 – 1 का गुणनखण्ड है।

x11 – 1 का शेषफल = (1)11 – 1 = 1 – 1 = 0

∴ (x – 1), x11 – 1 का गुणनखण्ड है।

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