To write : the function of the form
Answer to Problem 46E
Explanation of Solution
Given information :
Concept Involved:
For long division of polynomials by divisors of the form x - k, there is a shortcut
called synthetic division. The pattern for synthetic division of a cubic polynomial is
summarized below. (The pattern for higher-degree polynomials is similar.)
Synthetic Division (for a Cubic Polynomial): To divide
In case when we have a polynomial with a missing term, insert placeholders with zero coefficients for missing powers of the variable. Vertical pattern: Add terms in columns Diagonal pattern: Multiply results by k. This algorithm for synthetic division works only for divisors of the form x - k. Remember that |
The Division Algorithm : If
Calculation:
Set up the synthetic division to divide
If
Bring down the leading coefficient to the bottom row.
Multiply -2by the value just written on the bottom row. Place this value right beneath the next coefficient in the dividend:
Add the column created and write the sum in the bottom row:
Repeat until done. Multiply -2by the value just written on the bottom row. Place this value right beneath the next coefficient in the dividend:
Add the column created and write the sum in the bottom row:
Repeat until done. Multiply -2by the value just written on the bottom row. Place this value right beneath the next coefficient in the dividend
Add the column created and write the sum in the bottom row:
Write out the answer.The numbers in the last row make up your coefficients of the quotient as well as the remainder. The final value on the right is the remainder. Working right to left, the next number is your constant, the next is the coefficient for x , the next is the coefficient for x squared, and so on.
By dividing the given polynomial
Substituting -2 for
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
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