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On dividing x^33x^2+x+2 by a polynomial g(x), the quotient and remainder were x–2 and –2x+4, respectively. Find g(x).
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25/05/2021 1:05 pm
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On dividing x^{3}3x^{2}+x+2 by a polynomial g(x), the quotient and remainder were x–2 and –2x+4, respectively. Find g(x).
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25/05/2021 1:07 pm
Given,
Dividend, p(x) = x^{3}3x^{2}+x+2
Quotient = x2
Remainder = –2x+4
We have to find the value of Divisor, g(x) =?
As we know,
Dividend = Divisor × Quotient + Remainder
∴ x^{3}3x^{2}+x+2 = g(x)×(x2) + (2x+4)
x^{3}3x^{2}+x+2(2x+4) = g(x)×(x2)
Therefore, g(x) × (x2) = x^{3}3x^{2}+x+2
Now, for finding g(x) we will divide x^{3}3x^{2}+x+2 with (x2)
Therefore, g(x) = (x^{2}–x+1)
This post was modified 2 years ago by Raavi Tiwari
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