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Steps and examples for adding and subtracting polynomials. It includes instructions, sample problems, and links to khan academy resources. Useful for students preparing for accuplacer exams or learning algebra.
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TOPIC: Add and Subtract Polynomials
Anne Arundel County Public Schools Page 1 of 3
Khan Academy Link: https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials- topic/polynomial-basics-core-algebra/v/adding-and-subtracting-polynomials-
Steps to Add Polynomials: To add polynomials we simply add any like terms together.
Step 1: Arrange each polynomial with the term with the highest degree first then in decreasing order of degree.
Step 2: Group the like terms. Like terms are terms whose variables and exponents are the same.
Step 3: Simplify by combining like terms.
Sample Problem: Add the polynomials. (2x 2 + 6x +5) + ( 3x 2 โ 2x โ 1)
Step 1: The polynomials are in decreasing order of degree.
Step 2: Group the like terms.
2x 2 + 3x 2 + 6x โ 2x + 5 -
Step 3: Simplify by combining the like terms
2x 2 + 3x 2 + 6x โ 2x + 5 -
5x 2 + 4x + 4
TOPIC: Add and Subtract Polynomials
Anne Arundel County Public Schools Page 2 of 3
Steps to Subtract Polynomials:
To subtract Polynomials, first reverse the sign of each term we are subtracting (turn โ+โ into โ-โ, and โ-โ into โ+โ), then follow the previous steps to add polynomials.
Sample Problem: Subtract the polynomials.
5y^2 + 2xy โ 9 โ (2y 2 +2xy โ 3)
Step 1: Reverse the sign of each term we are subtracting.
5y^2 + 2xy โ 9 - (2y^2 + 2xy โ 3)
5y^2 + 2xy โ 9 + (-2y 2 - 2xy + 3)
Step 2: The polynomials are in decreasing order of degree.
Step 3: Group the like terms.
5y^2 โ 2y^2 +2xy โ 2xy โ 9 + 3
Step 4: Simplify by combining the like terms.
5y^2 โ 2y^2 +2xy โ 2xy โ 9 + 3
3y^2 โ 6
Now complete the four practice problems on the next page and check your answers!