Practice Objectives
- Demonstrate an understanding of polynomial long division
- Demonstrate the ability to write a single-variable polynomial in standard form
- Demonstrate the ability to divide polynomials using synthetic division
Practice Dividing by a Polynomial of the form (x - k) using Synthetic Division
Instructions:
Answer 7/10 questions correctly to pass.
Divide each using synthetic division. Write the quotient in the "Quotient" box and the remainder in the "Remainder" box. If there is no remainder, leave the remainder box empty or write 0.
Both the quotient and remainder must be written in standard form, otherwise your answer will be marked as incorrect.
Please read the items below for proper formatting.
- Rules for Exponents:
- Exponents can only be used with variables (e.g., x^2, x^3).
- Exponents must be single-digit positive integers (1, 2, 3, ..., 9). An exponent of zero is not allowed.
- Use the "^" key to raise a variable to a single-digit exponent (e.g., x^2, x^3).
- Rules for Numbers:
- Coefficients (numbers in front of variables) must be placed directly in front of the variables (e.g., 2x, -3x^2).
- Examples:
- 1x or x (implicitly 1)
- -7x
- 4x^2
- 9x^3
Problem:
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Synthetic Division:
- Write the dividend in standard form (descending powers of x)
- Under the long division symbol, place the coefficients of the dividend
- Use 0 as the coefficient for each missing term
- Find the appropriate divisor:
- For x - k, (k > 0), use k as the divisor
- Example: x - 3, divisor is 3
- For x + k, (k > 0), use -k as the divisor
- Example: x + 3, divisor is -3
- For x - k, (k > 0), use k as the divisor
- Leave space for two rows below the dividend and draw a horizontal line under the second row (middle row)
- Drop the first coefficient from the dividend directly into the third row (bottom row)
- Follow the pattern:
- Multiply the divisor by the number in the bottom row
- Place the product in the middle row of the next column
- Add the numbers in the column (middle and top row numbers), placing the sum in the bottom row
- Repeat until all columns are complete
- Write the result:
- The bottom row gives coefficients of the quotient, starting one degree lower than the dividend
- The last number in the bottom row is the remainder
- Verify your answer (optional):
- Multiply the quotient by the divisor and add the remainder. The result should equal the dividend
Step-by-Step:
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