Honors Algebra 2 (2nd Hour, Fall 2011): 1.3 Algebraic Expressions

Hi, it's Eleni. This section in the book has a TON of information so I'll try to shorten it as well as I can. First, it defined a lot of new terms.

Set: A collection of objects of some type

Elements: the objects in a set

Equal sets: sets contain exactly the same elements

Subset: other set contains all of its elements......pic........>>>>>>>>>>>

Constant: A letter or symbol that represents a specific element of a set

Variable: A letter or symbol that represents any element of a set

Algebraic expression: result obtained by applying additions, subtractions, multiplications, divisions, powers, or the taking of roots to this collection

Value: specific numbers subsituted for variables in an algebraic expression

Domain: consists of all real numbers that may represent the variables (assumed all real numbers when not specified)

monomial: algebraic expression consisting of one term

Binomial: sum of two monomials

Trinomial: sum of three monomials

Polynomial in x: Sum of form

Term: each expression a(sub k) x^k of the polynomial

Leading coefficient: coefficient of a(sub k) of the highest power of x

Equal polynomials: same degree and coefficients of like powers of x are equal

Zero polynomial: all coefficients of a polynomial are zero

POLYNOMIAL PRODUCTS

multiplying binomials

Foil is basically the destributive property in action. Both terms in the first binomial must be distributed to the second binomial.

Multiplying Polynomials

Any larger polynomials use the same concept. Take each term in the first polynomial and distribute it to all the other terms in the second polynomial. Note: These will get extensive, so try to keep it organized...

Dividing a polynomial by a monomial

Each term in the polynomial must divide by the monomial
Helpful Product formulas

FACTORING POLYNOMIALS
basics
Simply take common factors out of the expression. This is basically the distriutive property in reverse.
I hope you don't need a visual...
Helpful factoring formulas

Factoring trinomials

Trinomials take the form:

To factor this, you turn it into a product of two binomials.

When p= 1 the binomials will be (x+_) (x+_)

The missing numbers will be two factors of r that have a sum of q.

Remember: you can check your answer by multiplying it back out with foil.

Now something a little bit harder...when p doesn't equal 1.

To do this, you have to take factors of p and factors of r.

factors of p put on a column on the left and r in a column on the right. You cross multiply the factors and their sum will equal q. When this is correct (it's a guess and check method), you read the factors left to right to get the final binomials.