Concept explainers
(a)
The root or zero feature using graphical utility
(a)
Answer to Problem 75E
The zeros are 0, 3, 4 and around
Explanation of Solution
Given information:
The given function as shown below,
Formula used:
The horizontal axis is x axis and vertical axis is y axis.
Calculation:
Let us draw the graph of the function,
We can observe from the graph that the zeros are 0, 3, 4 and around
Conclusion:
The zeros are 0, 3, 4 and around
(b)
The exact value of one of the zeros.
(b)
Answer to Problem 75E
The exact zero of the function is x = 0, 3 and 4
Explanation of Solution
Given information:
The given function as shown below,
Formula used:
The one of the exact zero by putting
Calculation:
Let us find the one of the exact zero by putting
Hence, the exact zero of the function is x = 0, 3 and 4
Conclusion:
The exact zero of the function is x = 0, 3 and 4
(c)
The synthetic division based on the factor of the polynomial.
(c)
Answer to Problem 75E
The function will become
Explanation of Solution
Given information:
The given function as shown below,
Formula used:
Synthetic division is a nice shortcut for long division of polynomials by divisors of the form x-k-
Calculation:
Let us use the synthetic division to verify the result of part (b).
Synthetic division is a nice shortcut for long division of polynomials by divisors of the form x-k-
The pattern for synthetic division of a cubic polynomial is summarized below
First we will have to set up an array,
Divisor
Quotient
Let us again perform the test for another factor,
Divisor
Quotient
Hence, x = 3 and x = 4are factors of the given polynomial function.
Now, we can write the function as,
After factorizing the quotient,
Hence, after factorizing polynomial completely, the function will become
Conclusion:
The function will become
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- 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