Combining Polynomials Worksheet
Grade 10 math worksheet focusing on adding, subtracting, and multiplying polynomials, including real-world application problems.
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Combining Polynomials Worksheet
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Read each question carefully and follow the instructions to combine the polynomials. Show all your work for full credit.
Add the following polynomials. Write your answer in standard form.
1. (3x² + 5x - 7) + (2x² - 3x + 10)
2. (4y³ - 2y + 8) + (-y³ + 5y - 6)
Subtract the following polynomials. Write your answer in standard form.
3. (6m² - 2m + 9) - (3m² + 4m - 5)
4. (x³ + 7x² - 4x) - (5x³ - 2x² + x)
Multiply the following polynomials. Write your answer in standard form.
5. 3x(2x² - 5x + 4)
6. (x + 3)(x - 5)
7. (2y - 1)(y² + 3y - 4)
Complete the following sentences with the correct term.
8. A is a mathematical expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
9. When adding or subtracting polynomials, you combine .
Indicate whether each statement is True or False.
10. The degree of the polynomial 5x⁴ + 2x³ - 7x + 1 is 3.
True
False
11. When multiplying (x + 2) and (x - 2), the result is a binomial.
True
False
Solve the following word problem.
12. The length of a rectangle is represented by the polynomial (3x + 5) and its width is represented by (x - 2). Find a polynomial that represents the perimeter of the rectangle. Then, find a polynomial that represents the area of the rectangle.
Perimeter:
Area: