1. Polynomials!!! 

2. 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

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

4. 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

5. 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

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

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

8. 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

9. Polynomial Name by # of Terms Name by Degree12 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

10. 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….

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

12. 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

13. 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

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

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

16. 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

17. 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

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

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

20. y-intercepts
Where the graph crosses the y-axis

21. y-Intercept: (0,-12)

22. y-Intercept: (0,2)

23. 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

24. 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)

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