Q.1 ,Divide the polynomial p(x) by the polynomial g(x) where :-
p(x)= x^4 - 3x^2 +4x +5
g(x)= x^2 +1-x
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Given p(x) = x^4 - 3x^2 + 4x + 5 - > Dividend
Given g(x) = x^2 + 1 - x - > Divisor
Remainder = 8
Quotient = x^2 + x - 3
Now,
We know that Dividend = Divisor * Quotient + Remainder.
= > (x^2 + 1 - x) * (x^2 + x - 3) + 8
= > (x^4 + x^3 - 3x^2 + x^2 + x - 3 - x^3 - x^2 + 3x) + 8
= > x^4 - 3x^2 + 4x - 3 + 8
= > x^4 - 3x^2 + 4x + 5.
= > Dividend.
Hope this helps!
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