Let P(x)=8x4+6x2−3x+1 and D(x)=2x2−x+2. Find polynomials Q(x) and R(x) such that P(x)=D(x)⋅Q(x)+R(x).
Expert Community at Your Service
Solve your problem for the price of one coffee
The polynomials: P(x)=8x4+6x2−3x+1,D(x)=2x2−x+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+6x2−3x+1 by D(x)=2x2−x+2 is given by: According to division algorithm, we have, 8x4+6x2−3x+1=(2x2−x+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
Ask your question. Get your answer. Easy as that
Get answers within minutes and finish your homework faster
Or
Dont have an account? Register
Get access to 24/7 tutor help and thousands of study documents
Already have an account? Sign in