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