Algebra 2 Section 6.2 day 1
Classifying & Evaluating Polynomial Functions
Learning Target: I can classify polynomials & evaluate polynomial functions
at a given value. [F.IF.4]
A term is a number, variable, or a product of numbers and variables.
examples: ___________________________
- the sum or difference of many terms.
example:
4x3
3x2 + 5
–5x + 4xy + y
7x5 + x3 + 4y2 + 3
• polynomials can be classified by the number of terms.
Polynomial
• Always write in standard form
(exponents in ______________________ order).
Write the polynomials in standard form & classify by number of terms.
Polynomials...
2. 18a2 + 7a + 4a3 = __________________________
classify by terms ______________________
degree ____ classify by degree ____________________
1. –1 + 8k – k4 – 3k2 = ___________________________
classify by terms ______________________
degree ____ classify by degree ____________________
cubic
examples
Polynomials...• the highest exponent of a polynomial is called the _________
• can also be classified by the degree
5
2x
4x2 + 7
–x3 + 8x2 + 3x – 9
3x4 – 5x2
** go back to #1,2, state the degree and classify by the degree
A polynomial function is a function in the form:
f(x) = anxn + an-1xn-1 + ... + a1x + ao
- All exponents must be whole numbers
(cannot be negative, decimal, or fraction)
- no variables can be under radicals or in denominator
- All coefficients must be real numbers (no imaginary)
• an is the leading coefficient• a0 is the constant
A polynomial function must have ...
ex: f(x) = 4x3 + 6x2 - 5
Decide whether the function is a polynomial function. If it is, then write the function in standard form, state the degree, type and the leading coefficient.
1. f(x) = 4x2 - 5x-3
2. f(x) = -0.8x3 + x4 - 5
Yes or No
If yes, standard form ______________________
degree _____ type ______________
leading coeff. _____
If no, why? ______________________________
Yes or No
If yes, standard form ______________________
degree _____ type ______________
leading coeff. _____
If no, why? ______________________________
3. f(x) = 4 - √3 x - 5x2Yes or No
If yes, standard form ______________________
degree _____ type ______________
leading coeff. _____
If no, why? ______________________________
4. f(x) = - 3x + 8x1/2 Yes or No
If yes, standard form ______________________
degree _____ type ______________
leading coeff. _____
If no, why? ______________________________
One way to evaluate a polynomial is through direct substitution.
5. Evaluate f(x) = 5x3 + x2 - 4x + 1 when x = -1
6. Evaluate f(x) = 3x5 - x4 - 5x + 10 when x = 2
7. Evaluate f(x) = x4 - 5x2 + 10 when x = -2
Rally Coach
Assignment:worksheet 6.2
Alg 2 6.2 Day 1 Worksheet Answers1. Yes
f(x) = -2x3 + 3x2 + 4xDegree 3Cubicl.c. = -2
2. No because can't
have negative exponents
3. Yes
f(x) = √5x4 +3x2 - x -7
Degree 4
Quartic
l.c. = √5
4. Yes
f(x) = -1/6 x2 + 1/3x + 2/3
Degree 2
Quadratic
l.c. = -1/6
5. No because i is
not a real number
6. Yes
f(x) = -5x+7
Degree 1
Linear
l.c. = -5
7. Yes
f(x) = 11
Degree 0
constant
l.c. = 11
8. No variable can't
be under a root (fractional
exponent)
9. 28 10. -39
11. 9 12. 12
13. x9 14. 15. 27x6 16. 2
y2
5x4
2y2
17. 18. 19. 20.52x4
32y10
x30
625x8
3x6