Polynomials!!! 

POLYNOMIAL Function: A polynomial is the monomial or the sum of monomials with all exponents as whole numbers and coefficients are all real numbers. Ex- x3+6x2+12x+8

Is it a polynomial? YES a) NO b) NO c) YES d)

The terms of a polynomial are in STANDARD FORM when: they are ordered from left to right in ______________ order; which means from the ____________ exponent to the ____________ decreasing largest smallest

DEGREE: The _________exponent in the polynomial. It determines the _____________________. largest Number of Zeros Ex: The degree of –7x + 9 – 4x2 is ____ because ___ is the largest exponent in the polynomial. 2 2 Classifying: 0 – Constant 2 – Quadratic 4 - Quartic 1 – Linear 3 – Cubic

The ______________once in _________________. LEADING COEFFICIENT: The ______________once in _________________. first coefficient standard form CONSTANT: The term _________________ a variable. without

STANDARD FORM a. Standard Form: Leading Coefficient: Degree: Constant: b. Leading Coefficient: Standard Form: Constant: Degree:

B. Their _________ of terms C. Look at the chart for an explanation. Some polynomials have SPECIAL NAMES that are determined by the following: A. Their _________ or B. Their _________ of terms C. Look at the chart for an explanation. degree number

Polynomial Name by # of Terms Name by Degree 12 8x 4x2 + 3 5x3 + x2 3x2 – 4x + 6 7t4 – 7t + 3 Monomial 1 Constant 1 Monomial 1 Linear Binomial 2 2 Quadratic 2 Binomial 3 Cubic 3 Trinomial 2 Quadratic 3 Trinomial 4 Quartic

How do we write in interval notation? x < 2…. when you want include use a bracket [ when you want to exclude use a parenthesis ( Let’s draw a number line first….

Draw a number line first…. Let’s do another type…. Draw a number line first….

Domain Range all the y-values Read the graph from bottom to top all the x-values Read the graph from left to right Range all the y-values Read the graph from bottom to top

What is the domain of f(x)? Ex. 1 What is the domain of f(x)? (2,4) (-1,-5) (4,0) y = f(x) Domain

Ex. 2: What is the range of f(x)? (2,4) (-1,-5) (4,0) y = f(x) Range

With polynomials…. The DOMAIN is always All Reals, The RANGE will be: Lower Boundary to infinity, Negative infinity to Upper Boundary,

Zeros/x-intercepts/Solutions/Roots Where the graph crosses the x-axis What’s a zero? Zeros/x-intercepts/Solutions/Roots Where the graph crosses the x-axis

Where the graph crosses the x-axis. Also called zeros. Analyze the Graph of a Function x-intercepts Where the graph crosses the x-axis. Also called zeros. Zeros: 1, 5

X-Intercepts: (-2, 0) (-2, 0) (3,0) Zeros, Roots: x = -2, -2, 3

X-Intercepts – (-1,0)(1,0)(2,0) Zeros, Roots x = -1, 1, 2

y-intercepts Where the graph crosses the y-axis

y-Intercept: (0,-12)

y-Intercept: (0,2)

Y- int: (0, -1) # of zeros: 4 Y- int: (0, 15) # of zeros: 2 Find the y-intercepts & number of zeros: a) b) Y- int: (0, -1) # of zeros: 4 Y- int: (0, 15) # of zeros: 2

All reals All reals (-2,0)(-2,0)(1,0) (0, -4) Find the following Domain: Range: 3. x-intercepts: 4. y-intercepts: All reals All reals (-2,0)(-2,0)(1,0) (0, -4)

All reals [-4, ∞) -2, 2 (0, -4) Find the following Domain: Range: 3. Zeros: 4. y-intercepts: All reals [-4, ∞) -2, 2 (0, -4)