Polynomials

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Polynomials by Mind Map: Polynomials

1. Vocabulary

1.1. End behavior

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

1.2. Leading coefficient

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

1.3. Local maximum

1.3.1. The greatest value in a set of points.

1.4. Local minimum

1.4.1. The least value in set of points.

1.5. Monomial

1.5.1. Consisting of one term

1.6. Multiplicity

1.6.1. A large number

1.7. Polynomial

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

1.8. Polynomial function

1.8.1. real numbers and n are a non negative integer.

1.9. Synthetic division

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

1.10. Turning point

1.10.1. a time at which a decisive change in a situation occurs

2. Transforming polynomial function

2.1. Vertical=f(x)+K

2.2. Horizontal=F(x+h)

2.3. Vertical stretch=Af(x)

3. Investigating graphs of polynomial functions

3.1. Linear graph=degree 1

3.2. Quadratic graph=degree 2

3.3. Cubic graph=degree 3

3.4. Quartic graph=degree 4

3.5. Quintic graph=degree 5

4. Finding real roots of polynomial equations.

4.1. Use the zero product property tot find the zeros or solutions.

5. Fundamental theorem of algebra.

5.1. Use the Zero product property to find the solutions of the numbers and then factor the solutions.

6. Dividing polynomials

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

7. Factoring polynomials

7.1. 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.

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

8.1. 5x^3+15

8.1.1. The Leading coefficient would be 5 and the degree would be 3

9. Multiplying and monomial and a polynomial

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

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