How can we find the quotient and remainder when: f(x)=x^5−x^4−4x^3+2x+3 is divided by g(x)=x−2?

taumulurtulkyoy 2022-10-23 Answered
How can we find the quotient and remainder when:
f ( x ) = x 5 x 4 4 x 3 + 2 x + 3
is divided by
g ( x ) = x 2 ?
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Answers (1)

garbhaighzf
Answered 2022-10-24 Author has 13 answers
A practical method is as follow:
x 5 x 4 4 x 3 + 2 x + 3 x 2 x 4 4 x 3 + 2 x + 3 x 4 2 x 3 + 2 x + 3 x 3 4 x 2 + 2 x + 3 2 x 2 6 x + 3 4 x 9 6
so the quotient is x 4 + x 3 2 x 2 4 x 6 and the remainder is -9.
and to explain the procedure of calculus: we divide the leading term x 5 of the dividend by the leading term x of the divisor we find x 4 and then we calculate:
x 5 x 4 4 x 3 + 2 x + 3 x 4 ( x 2 ) = x 4 4 x 3 + 2 x + 3 = R ( x )
and repeat the same calculus using R(x) as your new dividend until we find the remainder R(x) with degree less than the degree of the divisor x-2.
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