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Polynomials Door Mind Map: Polynomials

1. Transforming polynomial function

1.1. Vertical =f(x)+K

1.2. Horizontal =f(x+h)

1.3. Vertical stretch =Af(x)

1.4. Factoring polynomials

1.4.1. X-A must equal 0 so to see if the given binomial is a factor of the polynomial you use synthetic substitution and if it equals 0 then it is a factor.

2. Multiplying and monomial and a polynomial

2.1. (x+2)(x^2+3x+5)

2.1.1. You multiply x by everything in the order parenthesis and then multiply 2 by everything in the other parenthesis and then you combine like terms.

3. Fundamental theorem of algebra.

3.1. Use the zero product property to find the solutions of the numbers and then factor the solutions.

4. The leading coefficient would be 5 and the degree would be 3.

5. Turning point

5.1. A time at which a decision change in a situation occurs.

6. Vocabulary

6.1. Multiplicity

6.1.1. A large number

6.2. Polynomial

6.2.1. Is the sum of one or more monomials with real coefficients and non negative integer exponents.

6.3. Polnomial function

6.3.1. A shorthand ,or shortcut , method of polynomial division in the case of dividing by a linear factor.

6.3.1.1. Real numbers and n are a non negative integer

6.4. Synthetic division

6.4.1. Leading coefficient

6.4.1.1. The numbers written in front of the variable with the largest exponent

6.5. End behavior

6.5.1. What is going on at the ends of each graph

6.6. Local maximum

6.6.1. The greatest value in a set of points.

6.7. Local minimum

6.7.1. The least value in set of points.

6.8. Monomial.

6.8.1. Consisting of one term.

7. Identifying the leading coefficient and the degree of a polynomial

7.1. 5x^3+15

8. Dividing polynomial.

8.1. You can either use long term division or synthetic division

9. Finding real roots of polynomial equations.

9.1. Use the zero product property to find the zeroes or solutions.

10. Investing graphs of polynomial functions

10.1. Linear graph =degree 1

10.2. Quadratic graph= degree 2

10.3. Cubic graph = degree 3

10.4. Quartic graph= degree 4

10.5. Quintic graph =degree 5