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Polynomials, Graph (complete factor form), If given two root, Grouping -…
Polynomials
Operations
Addition
Combine like terms
Subtraction
Subtract like terms
Multiplication
Use distribute property to each term,
Division
Long division
Divisor not constant
Fractions
Any Situation
Synthetic Divison
Degree greater > 2
Solving Polynomial equations
Use a CALCULATOR
Finding Roots
Real roots only
If given one root
Synthetic Division
Rational zero theorem
Repeat to find all zeros
Long Division
If not complete
Factor
Rational Zero Theorem
Repeat to find all real zeros
Complete the square
Imaginary Roots Involved
Conjugate
Synthetic Division
If not all zero were found
Rational Zero Theorem
Repeat to find all zeros
Grouping
Find all remaining zeros
Long Division
If not complete
Rational Zero Theorem
Find all zeros
Factor
Find all zeros
No roots given :(
Rational Zero Theorem
Synthetic Division
Repeat to find all real zeros
Grouping
Find all remaining zeros
After any method
Irreducible Polynomial
Quadratic
Complete the Square
Cubic or Higher degree
Substitute number
Plot points and graph
Connect points to estimate zero
Find Remainder
Remainder Theorem
f(x) / (x-a), the remainder = f(a)
Find Number of Roots
Descartes Theorem
Number of positive zeros
Number of negative zeros
Number of imaginary zeros
Graph (complete factor form)
Leading coefficient test
Test the end behavior of the function
Odd Degree
Leading Coefficient > 0
f(x) –> ∞ as x–> ∞
f(x) –> -∞ as x–> -∞
Leading Coefficient < 0
f(x) –> ∞ as x–> -∞
f(x) –> -∞ as x–> ∞
Even Degree
Leading Coefficient < 0
f(x) –> -∞ as x–> ∞
f(x) –> -∞ as x–> -∞
Leading Coefficient > 0
f(x) –> ∞ as x–> -∞
f(x) –> ∞ as x–> ∞
Multiplicity
The number of times when x is the root of the function
Graph
Odd: cross
Even: bounce
If given two root
Synthetic Division: Twice
If not all zeros were found
Rational Zero Theorem
Repeat to find all real zeros
Factor
Find all real zeros
Grouping
Find all remaining zeros
All zeros were found
Grouping
Find all remain zeros