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Polynomials by Mind Map: Polynomials

1. 3-1 Basics of Polynomials

1.1. Some people think about monomials when they see the word polynomial.The two go hand in hand.

1.1.1. Each monomial in a polynomial is a term.

1.2. Definition: A monomial or a sum or difference of monomials.

1.3. Polynomials have no variables in the denominator or exponent spot. The don't have roots (like square root) or absolute values of variables. All variables have whole numbers.

1.4. Important Terms

1.4.1. Polynomial

1.4.1.1. Definition stated above.

1.4.2. Monomial

1.4.2.1. A number or product with only one term; the term is a whole number.

1.4.3. Degree of a Polynomial

1.4.3.1. Given by the term with the highest degree.

1.4.4. Leading Coefficient

1.4.4.1. Coefficient of the first term.

1.4.5. Degree of a Monomial

1.4.5.1. Sum of the exponents or a variable.

1.4.6. A little hack: most words that end in -nomial and have a number start such as tri or bi just mean three terms, two terms, etc.

1.5. Examples of Polynomials

1.5.1. 5x^2

1.5.2. 0.20x^6

1.5.3. 2x^4-x^2

2. 3-2/3-4 Multiplying, Dividing, and more!

2.1. 3-2 Rules of Multiplying Polynomials

2.1.1. When multiplying two polynomials use distributive property.

2.1.2. Example!

2.1.2.1. (x-2)(1+3x-x^2)

2.1.2.1.1. : Write the polynomials in standard form. (x-2)(-x^2+3x+1)

2.1.2.1.2. : Distribute x then -2.

2.1.2.1.3. : Multiply then add the exponents.

2.1.2.1.4. : Combine the like terms.

2.1.2.1.5. : -x^3+5x^2-5x-2

2.1.3. Multiply each term in the second polynomial by the terms in the first.

2.2. 3-3 Rules of Dividing Polynomials

2.2.1. When dividing polynomials you use long division. It is the method used by dividing a polynomial by another polynomial of a lower term.

2.2.2. Important Vocab to remember!

2.2.2.1. Synthetic Division

2.2.2.1.1. Shorthand version of dividing a polynomial by a linear binomial using only the provided coefficients.

2.2.3. It looks very similar to normal long division, but this time you are using the smaller equations, such as x^2-2x^4.

2.3. 3-4 Rules of Factoring Polynomials

2.3.1. m

3. Finding Real Roots of Polynomials

4. m