Let P(x)=8x^4+6x^2-3x+1 and D(x)=2x^2-x+2. Find polynomials Q(x) and R(x) such that P(x)=D(x)\cdot Q(x)+R(x)

Tahmid Knox 2021-09-03 Answered

Let P(x)=8x4+6x23x+1 and D(x)=2x2x+2. Find polynomials Q(x) and R(x) such that P(x)=D(x)Q(x)+R(x).

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Expert Answer

wheezym
Answered 2021-09-04 Author has 103 answers

The polynomials:
P(x)=8x4+6x23x+1,D(x)=2x2x+2
To determine:
The polynomials Q(x) and R(x) such that P(x)=D(x)Q(x)+R(x)
Solution:
The long division of polynomial P(x)=8x4+6x23x+1 by D(x)=2x2x+2 is given by:
According to division algorithm, we have,
8x4+6x23x+1=(2x2x+2)(4x2+2x)+(7x+1)
So, Q(x)=4x2+2x and R(x)=7x+1
Conclusion:
Hence, Q(x)=4x2+2x and R(x)=7x+1

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