6.When a polynomial x4+x3−10x2−1 is divided by another polynomial, the quotient is x3−3x2+2x−8 and the...

Emerson Barnes

Emerson Barnes

Answered

2022-01-31

6.When a polynomial x4+x310x21 is divided by another polynomial, the quotient is x33x2+2x8 and the remainder is 31. Find the other polynomial.
Please type the answer, not in writing thank you

Answer & Explanation

stamptsk

stamptsk

Expert

2022-02-01Added 23 answers

Given
Polynomial (dividend) x4+x310x21
Remainder is 31
Polynomial (quotient) is x33x2+2x8
To find the other polynomial(divisor)
Using division Formula
Dividend=quotient×divisor+remainder
Rewriting the formula
Dividendremainder=quotient×divisor
Dividendremainderquotient=divisor
Hence
divisor=Dividentremainderquatient
Plugin the known values
Divisor =x4+x310x2131x33x2+2x8
divisor =x4+x310x2132x33x2+2x8
Factorising numerator
divisor =x33x2+2x8(x+4)x33x2+2x8
Canceling x33x2+2x8 from numerator and denominator
divisor =(x+4)
Hence other polynomial (divisor) =x+4
Conclusion
Hence the other polynomial which gives quotient x33x2+2x8 and remainder 31 on dividing polynomialx4x310x21 is x+4.
Hence the other polinomial (divisor) is x+4

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?