- Demonstrate an understanding of the product rule for exponents
- Demonstrate the ability to find the product of a monomial and a polynomial
- Demonstrate the ability to find the product of two or more polynomials
Practice Multiplying Polynomials
Instructions:
Answer 7/10 questions correctly to pass.
Find each product. 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 an 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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Multiplying Polynomials:
- Multiply each term from the first polynomial by each term of the second polynomial
- Combine all like terms to simplify the expression
- If there are more than two polynomials, multiply the product of the first two by the next polynomial, repeating the process as needed
- Write your answer in standard form
- For single-variable polynomials, standard form means arranging terms in descending powers of the variable
- There is no widely accepted standard form for polynomials with two or more variables
Step-by-Step:
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