Concept explainers
To perform polynomial division for the given questions and also derive a formula for the general polynomial division
Explanation of Solution
Given Information We have to perform polynomial division on
(a)
(b)
(c)
Calculation (a)
on dividing,
(b)
(c)
on dividing,
remainder = 0
quotient =
Conclusion
We observe that, on performing each division, remainder = 0 in each case and quotient varies as:
So, we get a pattern here,
highest power of 'x' in numerator that is ‘n’ decides the quotient as, if ,
Remainder = 0
Therefore, we can conclude that, on dividing
remainder = 0
and
quotient =
Let us test it for,
on performing, division we get
remainder = 0
and
quotient =
As it matches the derived formula, therefore our formula is correct for the polynomial division.
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning