1. Turn In
GHSGT Worksheet!!

2. Polynomial Functions
2.1 (M3)

3. What is a Polynomial? 1 or more terms
Exponents are whole numbers (not a fractional)
Coefficients are all real numbers (no imaginary #’s)
NO x’s in the denominator or under the radical
It is in standard form when the exponents are written in descending order.

4. Classification of a Polynomial
By Degree:
Degree
Name
Example
n = 0
constant 3
n = 1
linear
5x + 4
n = 2
quadratic
2x2 + 3x - 2
n = 3
cubic
5x3 + 3x2 – x + 9
n = 4
quartic
3x4 – 2x3 + 8x2 – 6x + 5
n = 5
quintic
-2x5 + 3x4 – x3 + 3x2 – 2x + 6
Three Terms:
Trinomial
3+ Terms:
Polynomial
One Term:
Monomial
Two Terms:
Binomial
By Number of Terms:

5. Classify each polynomial by degree and by number of terms.
a) 5x + 2x3 – 2x2
b) x5 – 4x3 – x5 + 3x2 + 4x3
c) x2 + 4 – 8x – 2x3
d) 3x3 + 2x – x3 – 6x5
e) 2x + 5x7
quintic trinomial
cubic polynomial
Not a polynomial
cubic trinomial
quadratic monomial
7th degree binomial

6. EXAMPLE 1
Identify polynomial functions
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.
a. h (x) = x4 – x2 + 3 1 4
SOLUTION
Yes it’s a Polynomial.
It is in standard form.
Degree 4 - Quartic
Its leading coefficient is 1.

7. EXAMPLE 1
Identify polynomial functions
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.
SOLUTION
b. Yes it’s a Polynomial.
Standard form is
Degree 2 – Quadratic
Leading Coefficient is

8. EXAMPLE 1
Identify polynomial functions
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.
c f (x) = 5x2 + 3x –1 – x
SOLUTION
c. The function is not a polynomial function
because the term 3x – 1 has an exponent that is not
a whole number.

9. EXAMPLE 1
Identify polynomial functions
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.
d. k (x) = x + 2x – 0.6x5
SOLUTION
d. The function is not a polynomial function
because the term 2x does not have a variable
base and an exponent that is a whole number.

10. GUIDED PRACTICE
for Examples 1 and 2
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.
f (x) = 13 – 2x
p (x) = 9x4 – 5x – 2 + 4
not a polynomial function
polynomial function;
f (x) = –2x + 13;
degree 1, type: linear,
leading coefficient: –2
h (x) = 6x2 + π – 3x
polynomial function;
h(x) = 6x2 – 3x + π ;
degree 2, type: quadratic,
leading coefficient: 6

11. What do we do first to evaluate this?
EXAMPLE 2
Evaluate by direct substitution
Use direct substitution to evaluate f (x) = 2x4 – 5x3 – 4x + 8 when x = 3.
f (x) = 2x4 – 5x3 – 4x + 8
Write original function.
f (3) = 2(3)4 – 5(3)3 – 4(3) + 8
Substitute 3 for x.
= 162 – 135 –
What do we do first to evaluate this?
= 23
PEMDAS

12. 5 9 GUIDED PRACTICE for Examples 1 and 2
Use direct substitution to evaluate the polynomial function for the given value of x.
f (x) = x4 + 2x3 + 3x2 – 7; x = –2 5
g(x) = x3 – 5x2 + 6x + 1; x = 4 9

13. Graph Trend based on Degree
Even degree - end behavior going the same direction
Odd degree – end behavior (tails) going in opposite directions

14. Graph Trend based on Leading Coefficient
Positive
Odd degree—right side up, left side down
Even degree—both sides up
Negative
Odd degree—right side down, left side up
Even degree—both sides down

15. Symmetry: Even/Odd/Neither
First look at degree
Even if it is symmetric respect to y-axis
When you substitute -1 in for x, none of the signs change
Odd if it is symmetric with respect to the origin
When you substitute -1 in for x, all of the signs change.
Neither if it isn’t symmetric around the y axis or origin

16. Tell whether it is even/odd/neither
f(x)= x2 + 2
f(x)= x2 + 4x
f(x)= x3
f(x)= x3 + x
f(x)= x3 + 5x +1

17. Additional Vocabulary to Review
Domain: set of all possible x values
Range: set of all possible y values
Symmetry: even (across y), odd (around origin), or neither
Interval of increase (where graph goes up to the right)
Interval of decrease (where the graph goes down to the right)
End Behavior: f(x) ____ as x+∞
f(x) ______ as x-∞

18. Math 3 Book Page 67 #1 – 4 Page 68 #5 – 7 Page 69 #1 – 5, 8 – 16
a) Classify by degree and # of terms
b) Even, Odd or Neither
c) End Behavior

19. Blue Algebra 2 Books P.429 # 4 –10 #9 and 10 A) Domain and Range
B) Classify by degree and # of terms
C) Even, Odd or Neither
D) End