Algebra 2 honors (unit 2: polynomials and rational functions)

Polynomial

A sum of terms in the form of a real number coefficient times a variable raised to a whole number non-negative exponent.

Degree of a polynomial

The highest exponent of a polynomial.

Leading coefficient

The coefficient of the highest-degree term in a polynomial.

End behavior (even degree + positive leading coefficient)

Both ends of the graph face up (touchdown).

End behavior (even degree + negative leading coefficient)

Both ends of the graph face down (anti-touchdown).

End behavior (odd degree + positive leading coefficient)

Left end down and right end up (disco).

End behavior (odd degree + negative leading coefficient)

Left end up and right end down (anti-disco).

Zeros/roots

Values where f(x)=0; these correspond to x-intercepts on the graph.

Multiplicity of a zero (even)

If a zero has an even multiplicity, the graph touches the x-axis.

Multiplicity of a zero (1)

If a zero has a multiplicity of 1, the graph crosses the x-axis.

Multiplicity of a zero (odd, not 1)

If a zero has an odd multiplicity (that's not 1), the graph flattens out.

Turning points

The maximum number of turning points of a polynomial is one less than its degree. a point where the graph changes direction, either from increasing to decreasing or decreasing to increasing

y-intercept of a polynomial

The value of the polynomial when x=0, which corresponds to the constant term. the point where the graph crosses the y-axis

Greatest Common Factor (GCF)

The largest factor common to all terms in a polynomial.

Difference of squares

The factorization of a²-b² as (a+b)(a-b).

Sum of cubes

The factorization of a³+b³ as (a+b)(a²-ab+b²).

Difference of cubes

The factorization of a³-b³ as (a-b)(a²+ab+b²).

Factoring quadratics

Using methods like AC method or quadratic formula to factor quadratic expressions.

Remainder theorem

The remainder when dividing f(x) by (x-a) is f(a); if f(a)=0, then (x-a) is a factor.