Precalc Vocab 2

Polynomial

An expression of terms with variables raised to whole number powers

Degree of a Polynomial

The highest power of xxx

Leading Coefficient

The coefficient of the highest-degree term

Constant Term

The term with no variable

Greatest Common Factor

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 patter: a² - b²= (a+b) (a-b)

Cubic/ Quartic/ Quintic

Polynomials of degree 3, 4, and 5, respectively

Zero of a Function

Value that makes a function zero

Root

Another name for a zero

Multiplicity

Number of times a zero is repeated

Polynomial Inequality

Inequality involving a polynomial (>, <, less than or equal to, greater than or equal to)

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 Divison

Shortcut for dividing by a linear divisor like x-cx-cx-c

Factor Theorem

If f© = 0f© = 0f© = 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 → positive or negative infinity \ to \pm\inftyx → Positive or negative infinity 

Relative Maximum

A high 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:

Even degree, positive coefficient→ both ends up

Even degree, negative coefficient → both ends down

Odd degree, positive coefficient → left down, right up

Odd degree, negative coefficient → left up, right down

Intercepts

x intercept (s): where f(x)= 0 f(x)= 0f(x)=0

y intercept: where x= 0x = 0x=0