This study guide covers polynomials, including classifying polynomials by degree and terms, adding and subtracting polynomials, multiplying polynomials, dividing polynomials using long division and synthetic division, factoring quadratics, solving quadratics, and graphing quadratics by finding the vertex, axis of symmetry, and x-intercepts. Key concepts are polynomials having only positive integer exponents, the degree being the highest exponent, and the leading coefficient being the coefficient of the term with the highest exponent.

1. Algebra 2
Test 3 Study Guide
Polynomials only have positive, integer exponents.
Classifying polynomials
Monomial one term Constant degree of 0
Binomial two terms Linear degree of 1
Trinomial three terms Quadratic degree of 2
Polynomial four or more terms Cubic degree of 3
Quartic degree of 4
What is the degree of a polynomial? Highest exponent
What is the leading coefficient of a polynomial? Coefficient of term with highest
exponent
Adding and subtracting polynomials
Find and .
and
and
Multiplying polynomials
Dividing polynomials – long division and synthetic division
Factoring quadratics

2. Solving quadratics
Graphing quadratics
Find the vertex, axis of symmetry, and x-intercepts for each graph. If there are no x-
intercepts, say so.
vertex: (0,1) vertex: (0, -3)
axis of symmetry: 0 axis of symmetry: 0
nox-intercepts

3. x-intercepts: 3 and -1 x-intercepts: 2 and -2
axis of symmetry: 1 axis of symmetry: 0
vertex: (1, -4) vertex: (0, -8)
axis of symmetry: 1 axis of symmetry: -1
vertex: (1, -1) vertex: (-1, -4)