Review polynomials
Distributive property
Distributive property:
You multiply what is outside the parenthesis to everything that is inside the parenthesis.
Example:
Special case: Distributing a negative means negating everything inside the parenthesis.
Simplify:
Simplify:
New concept 8.1: Find the degree of a monomial.
Degree of a monomial:
The degree of a monomial the sum of the exponents of its variables.
Example: The degree of is 5+8+2 = 12.
Find the degree:
Degree of a monomial
New concept 8.1: Find the degree of a polynomial.
The degree of a polynomial is the degree of the highest degree term.
The degree of the polynomial is 3, because the highest power of the variable “x” is 3.
Simplify and find the degree and number of terms:
Adding and subtracting polynomials
To add two polynomials, add all of the like terms.
Example:
To subtract two polynomials, first negate the terms in the second polynomial and then add like terms.
Example:
Simplify
New concept 8.2: Greatest Common Factor (GCF) of a polynomial.
To find the GCF of the terms of a polynomial, do prime factorization of each term and find the common factors.
Example:
The first term factors as
The second term factors as
In both terms you see
So the GCF =