Notes 4.2 Classifying Polynomials.notebook
4.1 Answers
November 04, 2014
Notes 4.2 Classifying Polynomials.notebook
November 04, 2014
Notes 4.2: Classifying Polynomials
Polynomial Function: a function in which all exponents are whole numbers and the coefficients are real numbers
Leading Coefficient: an; the # in front of the first term
Degree: the highest exponent; classifies the polynomial
Constant: a0; the # without a variable
Standard Form: terms written in descending order based on the exponents
Notes 4.2 Classifying Polynomials.notebook
November 04, 2014
Classifying Polynomials
Degree
Type
Example
0
Constant
f(x) = 2
1
Linear
f(x) = ­x + 1
2
Quadratic
f(x) = ­3x2 + 2x ­ 7
3
Cubic
f(x) = 6x3 + x2 ­ 2x + 1
4
Quartic
f(x) = x4 ­ 1
5 or more Polynomial f(x) = ­5x6 + 3x5 + x4 ­ 10x2
Notes 4.2 Classifying Polynomials.notebook
November 04, 2014
Decide whether the polynomial is a function. If it is, write the function in standard form and state its degree, type, leading coefficient, and constant.
1.
2.
Standard form:
Standard form:
Degree:
Degree:
Type:
Type:
Leading Coefficient:
Leading Coefficient:
Constant:
Constant:
Notes 4.2 Classifying Polynomials.notebook
November 04, 2014
Decide whether the polynomial is a function. If it is, write the function in standard form and state its degree, type, leading coefficient, and constant.
3.
4.
Standard form:
Standard form:
Degree:
Degree:
Type:
Type:
Leading Coefficient:
Leading Coefficient:
Constant:
Constant:
Notes 4.2 Classifying Polynomials.notebook
November 04, 2014
Even and Odd Polynomial Functions
A function is EVEN if it has y­axis symmetry or has all even exponents.
*no exponent = even
A function is ODD if it has origin symmetry or has all odd exponents.
*exponent of 1 = odd
Notes 4.2 Classifying Polynomials.notebook
Even and Odd Polynomial Functions ­ HONORS ONLY
A function is EVEN if f(x) = f(­x)
A function is ODD if f(x) = ­f(­x)
November 04, 2014
Notes 4.2 Classifying Polynomials.notebook
November 04, 2014
Determine if the polynomial function is even, odd, or neither.
*Honors ­ prove using the definition*
5. f(x) = 3x2 + 2
8. f(x) = x4 ­ x2
6. f(x) = ­3x3 ­ 5x
9. f(x) = ­3x2 + 2x ­ 7
7. f(x) = 5x7 + 8x5 + x3 ­ 2x
10. f(x) = 5x­1 + 3x2 + 2
Notes 4.2 Classifying Polynomials.notebook
Polynomial Operations Review
Find the sum or difference
11. (2x4 + 3x2) + (­7x4 ­ 6x2)
12. (­3x5 + 2x3 + 1) ­ (­x5 ­ x4 + 8x3 + 5x)
13. (4x3 + 2x2 ­ 9) ­ (5x3 ­ 6x2 + 5)
14. (x4 + 3x2 ­ 2) + (4x4 ­ 5x2 + x + 3)
November 04, 2014
Notes 4.2 Classifying Polynomials.notebook
Now you try!
Find the sum or difference
15. (­5x4 ­ 2x2) + (­x4 + 3x2 ­ 1)
16. (x3 + 5x5 ­ 9x) ­ (­x5 + 2x4 + 4x3 + 5x)
November 04, 2014
Notes 4.2 Classifying Polynomials.notebook
November 04, 2014
Polynomial Operations Review
Find the product.
17. (2x + 1)(x ­ 4)
19. (x ­ 2)(3x2 + 6x ­ 4)
18. (3x ­ 2)2
20. (­x2 + 2)(x3 ­ x2 + 5)
Notes 4.2 Classifying Polynomials.notebook
Your turn! Find the product.
21. (2x + 1)(x3 + 2x2 ­ 4)
22. (x ­ 9)(4x2 ­ 6x + 1)
November 04, 2014