The document discusses multiplying polynomials, defining them as expressions with variables, constants, and exponents combined using addition, multiplication, but not division. It provides the steps to multiply polynomials using the FOIL method of multiplying the First, Outer, Inner, and Last terms. Examples are given of multiplying different binomial and trinomial expressions, and polynomials are noted as being used in fields like chemistry, electronics, and finance.

1. Multiplying Polynomials (x+4) (x+5)

2. Definitions Polynomials- an expression made with constants, variables, and exponents which are combined using addition, subtraction, and multiplication NOT DIVISION. Binomial -a mathematical expression consisting of two terms connecting by a plus sign or minus sign. Example: 2x+2 Trinomial- 3 monomials added or subtracted together. 2b*y+4 Term- A mathematical expression which may form a separable part of an equation, a series, or another expression. summed terms, each term consisting of a constant multiplier and one or more variables raised to any power

3. Steps (x+2) (x+4) 1. When starting always start with first term so X*X + X*4= X +4x 2. now you start with the second term in the first binomial so now you start with the two. 2*X + 2*4

4. FOIL (x+5) (x+6) FIRST X*X OUTER X*6 INNER 5*X LAST 5*6 X +6x+5x+30 X +11x+30

5. Examples 1. (x+10) (x+3) 2. (b+9) (b-2) 3. (y-3) (y-6)

6. Used in life can be used in chemistry, of gas equation example PV=nRt that is the gas law. Electronics use many polynomials as of resistance V=IR is a polynomial relating to the resistance from a resistor. And with the aim of finding equivalent liquid ( present, cash, or in hand value)