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Question -

यदि x3 – 3x2 + x + 2 को एक बहुपद g(x) से भाग देने पर, भागफल और शेषफल क्रमश: x – 2 और – 2x + 4 हैं तो g(x) ज्ञात कीजिए।



Answer -

दिया है : भाज्य p(x)= x3 – 3x2 + x + 2
भागफलq(x) = x – 2,
शेषफलr(x) = -2x + 4
भाजकg(x) = ?
भाज्य = भाजक × भागफल + शेषफल
p(x) = g(x) × q(x) + r(x)
x3 – 3x2 + x + 2 = g(x) (x – 2) + (- 2x + 4)
x3 – 3x2 + x + 2 + 2x – 4 = g(x) (x – 2)
g(x) (x – 2) = x3 – 3x2 + 3x – 2

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