Polynomial Operations — SAT Math Explained
The arithmetic operations (addition, subtraction, multiplication) applied to polynomials — expressions with multiple terms, each being a product of a coefficient and a variable raised to a whole-number power.
The Core Idea
Polynomials behave like 'super-numbers' — they follow all the same rules as regular arithmetic. Adding polynomials combines like terms; multiplying uses distribution and FOIL.
Key Vocabulary
An expression with one or more terms: monomials, binomials, trinomials
The highest exponent in the polynomial — determines the type and behavior
The coefficient of the highest-degree term
Terms with the same variable raised to the same power — these can be combined
Writing a polynomial with terms in order of decreasing degree
Operations
Combine like terms only — group by degree and add coefficients
Distribute the negative sign across the subtracted polynomial first, then combine like terms
Distribute the monomial to every term in the polynomial
Use FOIL: First, Outer, Inner, Last — then combine like terms
Distribute each term of the first polynomial to every term of the second
Degree Rules
The degree of the result is the same as the highest-degree input
The degree of the product is the sum of the degrees of the factors
Common Errors to Avoid
Adding exponents when adding polynomials (only combine coefficients of like terms)
Forgetting to distribute the negative sign in subtraction
Missing the 'Outer' and 'Inner' products in FOIL
Practice: Polynomial Operations
5 SAT-style questions. Select your answer and get an instant explanation.
Simplify: (3x² + 2x - 5) + (x² - 4x + 1)
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