Unit 2 Vocab: Polynomial Equations, Inequalities, and Graphs

For FHUS Pre-Calculus

Polynomial

An expression of terms with variables raised to whole number powers.

Degree of a Polynomial

The highest power of x³

Leading Coefficient

The Coefficient of the highest-degree term

Constant Term

The term with no varible

Greatest Common Factor (GCF)

The largest factor shared by all terms

Factoring by Grouping

Method to factor when there are four or more terms.

Difference of Squares

Special factoring pattern

Cubic / Quartic / Quintic

Polynomials of degree 3,4, and 5, respectively

Zero of a Function

Value that makes a function zero

Root/Solution

Another name for a zero

Multiplicity

Number of times a zero is repeated

Polynomial Inequality

Inequality involving a polynomial (>,<,≥,≤)

Sign Chart / Sign Analysis

Testing intervals between zeros to determine where a polynomial is positive or negative.

Interval Notation

Notation for solution sets of inequalities

synthetic division

shortcut for diving by a linear divisor like x-cx-cx-c

Factor theorem

If f(c)=0f(c) = 0f(c)=0, then x-cx-cx-c is a factor of f(x)f(x)f(x)

Remainder theorem

The remainder from dividing

End behavior

direction of the graph as x→∓∞x / to / pm / inftyx → ∓∞

Relative Maximum

A high point compared to nearby values

Relative Minimum

A low point compared to nearby values

Absolute Maximum

The highest point on the entire graph.

Absolute Minimum

the lowest point on the entire graph

Point of inflection

where the graph changes concavity

concavity

curving upward (concave up) or downward (concave down)

Intervals of Increase/Decrease

Where the function’s values rise or fall.

Leading coefficient test

Determines end behavior

Intercepts

X-intercepts: Where f(x)=0f(x)=0f(x)=0

Y-intercept: Where x=0x=0x=0