- Demonstrate the ability to find the sum or difference of polynomials
- Demonstrate the ability to perform mixed operations with polynomials
- Demonstrate the ability to write a single-variable polynomial in standard form
Practice Finding the Sum or Difference of Polynomials
Instructions:
Answer 7/10 questions correctly to pass.
Perform each indicated operation. Write your answer in standard form for single-variable polynomials.
Note: For single-variable polynomials, standard form means arranging terms in descending powers of the variable.
Correct Example: $$5x^2 + 2x - 1 \, ✅$$
Wrong Example: $$2x - 1 + 5x^2 \, ❌$$
Note: There is no widely accepted standard form for polynomials with two or more variables. For consistency in this exercise, it is suggested that you arrange the terms in descending degrees (prioritizing the term with the larger exponent on "x" when there is a tie), but any valid order will be scored as correct.
Correct Example: $$5x^2y + 2xy - 1 \, ✅$$
Alternative Order (also marked correct): $$2xy + 5x^2y - 1 \, ✅$$
Please read the items below for proper formatting.
- Rules for Exponents:
- Exponents can only be used with variables (e.g., x^2, y^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, y^3).
- Rules for Numbers:
- Coefficients (numbers in front of variables) must be placed directly in front of the variables (e.g., 2x, -3y).
- Examples:
- 1x or x (implicitly 1)
- -1y or -y (implicitly -1)
- 2x
- 2x^2
- 2x^3y^4
Problem:
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Adding Polynomials:
- Combine all "like terms"
- Write in standard form (single-variable case only):
- Arrange terms in descending powers of the variable
Subtracting Polynomials:
- Change the subtraction problem into an addition problem:
- Use the rule a - b = a + (-b)
- Keep the first polynomial the same
- Apply the negative sign to each term inside the second polynomial (distribute the negative)
- Combine all "like terms"
- Write in standard form (single-variable case only):
- Arrange terms in descending powers of the variable
Step-by-Step:
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