Polynomials
A polynomial is an expression with variables and coefficients using addition, subtraction, and non-negative integer exponents.
Vocabulary
Degree: highest exponent. Leading coefficient: coefficient of the highest-degree term.
Monomial (1 term), Binomial (2 terms), Trinomial (3 terms).
Adding & Subtracting
Combine like terms — same variable and exponent.
(3x² + 2x − 1) + (x² − 5x + 4) = 4x² − 3x + 3
Multiplying (FOIL for Binomials)
FOIL: First, Outer, Inner, Last
(x + 3)(x − 2) = x² − 2x + 3x − 6 = x² + x − 6
Special Products
(a + b)² = a² + 2ab + b²
(a − b)² = a² − 2ab + b²
(a + b)(a − b) = a² − b² (difference of squares)
Factoring
GCF first, then factor the remaining trinomial or use difference of squares.
2x² − 8 = 2(x² − 4) = 2(x+2)(x−2)
FAQ
Is 3/x a polynomial? No — exponents must be non-negative integers. Negative exponents disqualify it.
Quick Quiz
Test what you just learned. Choose the best answer for each question.