Math Problem Statement
Solution
To solve for the function using synthetic division:
-
Set up synthetic division: Write the coefficients of the polynomial: . The divisor is , so we use for synthetic division.
-
Perform synthetic division:
- Bring down the first coefficient (1).
- Multiply by the value brought down and add to the next coefficient.
- Repeat this process for all coefficients.
The steps are:
2 | 1 -2 4 3
| 2 0 8
-----------------
1 0 4 11
- Interpret the result:
- The last value in the bottom row is the remainder. For synthetic division, the remainder is .
Thus, .
Would you like a breakdown of each step or have additional questions?
Here are 5 related questions:
- How is synthetic division related to evaluating polynomials?
- What is the significance of the remainder in synthetic division?
- How would the process change if the root was ?
- Can synthetic division be used for polynomials of higher degrees?
- How does synthetic division help in factoring polynomials?
Tip: Synthetic division is also useful for checking if a value is a root of a polynomial!
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Synthetic Division
Formulas
Synthetic division process
Theorems
Remainder theorem
Suitable Grade Level
Grades 9-12
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