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Classifying and Analyzing Polynomials, Lecture notes of Pre-Calculus

University of Texas Southwestern Medical CenterPre-Calculus

Instructions on how to classify polynomials based on their degree, type, and leading coefficient. It includes examples of polynomial functions, their degrees, types, and leading coefficients. Additionally, it covers adding and subtracting polynomials and determining the number of real zeros. Students are encouraged to practice identifying the degree, type, and leading coefficient of polynomials, as well as finding the number of real zeros.

Typology: Lecture notes

2021/2022

Uploaded on 09/27/2022

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6.1ClassifyPolynomials
Notes6.1Polynomials

•
Mono
mial
One
Term
Example:5x
3
•
Poly
nomialSumorDifferenceof
Many
Terms
Example:5x
3
+8x
2
+3x17
MusthavewholenumberexponentsNotPolynomial:5
x
orx
1
NovariablesindenominatorNotPolynomial:
NosquarerootsofvariablesNotPolynomial:
NoabsolutevalueofvariablesNotPolynomial:

•
DegreeofaMonomial(oneterm):
sumoftheexponents
•
DegreeofaPolynomial:
Lookforthe
termwiththehighestpower
.

LeadCoefficient
isthecoefficientoftheterm
withhighestpower.

Whatistheleadcoefficientoftheexampleabove?


5x
3
+8x
2
+3x17
degree=
IdentifyingtheDegree
degree=
pf3
pf4

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Download Classifying and Analyzing Polynomials and more Lecture notes Pre-Calculus in PDF only on Docsity!

Notes 6.1 Polynomials

  • Monomial One Term Example: 5x^3
  • Polynomial Sum or Difference of Many Terms Example: 5x^3 + 8x^2 + 3x 17 Must have whole number exponents Not Polynomial: 5 x^ or x^1 No variables in denominator Not Polynomial: No square roots of variables Not Polynomial: No absolute value of variables Not Polynomial:
  • Degree of a Monomial (one term): sum of the exponents
  • Degree of a Polynomial:

Look for the term with the highest power.

Lead Coefficient is the coefficient of the term

with highest power.

What is the lead coefficient of the example above?

5x

3

+ 8x

2

+ 3x 17

degree=

Identifying the Degree

degree=

Common Polynomial Functions

Degree Type Example

0 constant f(x)=

1 linear f(x)=

2 quadratic f(x)=

3 cubic f(x)=

4 quartic f(x)=

Is it a polynomial function? If so, tell degree, type and leading coefficient. A. f(x) = (^) ½x 2 3x 4 4 B. g(x) = x 3

  • 3 x C. f(x) = 6x 2 +2x 1
  • x 4/ D. f(x) = 4x (^) √ 5 x 2

C. h(x) = x

4

8x

2

+ 1 D. k(x) = x

4

+ x

3

x

2

+ 2x 3

Degree: Type: Lead Coefficient:

Real Zeros:

Degree: Type: Lead Coefficient:

Real Zeros:

Assignment: Section 6.1, Pg 410 Problems #613, 1518, 28, 29, 3235