1. Calculate the Power of a Power
1.1. The base stays the same exponents are multiplied.
1.1.1. Example: (3^3)^3=3^9
2. Variable
2.1. A letter that represents a value that can change.
2.1.1. Example: x
3. Term
3.1. A number, variable or exponent
3.1.1. Examples: 3, x, 3x, 3^3, 3x^3
4. Constant Term
4.1. A term that does not have any variables.
4.1.1. Example: 5
5. Monomial
5.1. A polynomial with one term.
5.1.1. Example: 3x
6. Trinomial
6.1. A polynomial with three terms.
6.1.1. Example: 1+7x-3x
7. Unlike Terms
7.1. Different variables or same variables with different exponents.
7.1.1. Example: 3x and 3y are Unlike Terms
8. Dividing Polynomials with Different Base
8.1. Divide the constant terms and subtract the variables.
8.1.1. 10 a^5/5 a^2=2 a^3
9. Adding Polynomials
9.1. With Same Variable
9.1.1. Variable stays the same and the constants are added.
9.1.1.1. Example: 7x^5+6x^5=13x^5
9.2. With Different Variable
9.2.1. You cannot add two polynomials with different variables as both terms need to be like terms in order to be able to be added.
10. Multiplying Polynomials with Same Base
10.1. The base stays the same and the exponents are added.
10.1.1. Example: 7^2+7^4=7^6
11. Dividing Polynomials with Same Base
11.1. The base stays the same and the exponents are multiplied.
11.1.1. Example: 7^5/7^2=7^3
12. Coefficient
12.1. The number part of a term.
12.1.1. Example: 8x, 8 is the Coefficient
13. Degree
13.1. Of a single term
13.1.1. Sum of the degrees in the term.
13.1.1.1. Example: 3^5, 5 is the Degree of this Term
13.2. Of a polynomial
13.2.1. Highest degree in the polynomial.
13.2.1.1. Example: 7^2+8^4, 4 is the Degree of this Polynomial
14. Binomial
14.1. A polynomial with two terms.
14.1.1. Example: 2x+3
15. Like Terms
15.1. Same variables and same exponents.
15.1.1. Example: 3x and 4x are Like Terms
16. Distributive Property
16.1. Simplifying an equation by combining like terms.
16.1.1. Example: 7x-3x=4x
16.1.2. Example: 3x (4x+2)=12x^2+6x
17. Subtracting Polynomials
17.1. With same variable
17.1.1. Example: 7x^5-3x^5=4x^5
17.1.2. The variable stays the same and the constants are subtracted.
17.2. With different variable
17.2.1. You cannot subtract polynomials with different variables as both terms must be like terms in order to subtract.
18. Constants With the Exponent of 0
18.1. Any constant to the exponent of 0 is equal to 1.
18.1.1. Example: 5^0=1