Section 1.3

Hey 5th Hour! Sorry this post is a day late...polynomials make me want to punch a wall, and I wanted to wait until we discussed them in class before I wrote about them on the internet. The wheel picked me to write a moderately short blog post about a 12 page section so I'll (try to) be brief.

First, theres two super important words that you need to know, not only for this section, but for the rest of this course:

A letter or symbol that represents any element of a set

The result obtained by applying additions, subtractions, multiplications, divisions, powers, or taking the roots to a collection

...and here's some other terms for this section:

Binomial: the sum of two monomials

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

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

Elements: the objects in a set

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

Equal Sets: sets contain exactly the same elements

Leading Coefficient: coefficient of a sub k of the highest power of x

Monomial: algebraic expression consisting of one term

Polynomial of X: Sum of form

Set: A collection of objects of some type

Subset: other set contains all of its elements

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

Trinomial: sum of three monomials

Value: specific numbers subsituted for variables in an algebraic expression

Zero Polynomial: all coefficients of a polynomial are zero

How to Add or Subtract Polynomials

How to Multiply Polynomials

FOIL Method

How to Divide Polynomials by a Monomial

Special Product Formulas

These cases appear so often, they deserve special attention. MEMORIZE THEM!

How to Factor Polynomials

Factoring is just like multiplying polynomials...except, it's not at all. It's the literal opposite.

Here's some factoring formulas to help you out a bit. MEMORIZE THESE TOO!

A factorization of a trinomial px^2 + qx + r, where p, q, and r are integers, must be of the form

px^2 + qx + r = (ax + b)(cx + d)

where a, b, c, and d are integers. It follows that

ac = p bd = r and ad + bc = q.

The LONG and TEDIOUS Guess and Check Method:

Factoring by Grouping:

Let's take 4ac + 2bc - 2ad - bd.

First, we group the first to terms and the last to terms.

4ac + 2bc - 2ad - bd = (

4ac + 2bc) - (

2ad + bd)

Now, we'll factor out the common variables and coefficients.

= 2c(2a + b) - d(2a + b)

Look at that! See what we did there? Now, after factoring out k, with k=2a + b, we get our final answer:

= (2c - d)(2a + b)

Factoring by grouping. Boom.

That's all, folks. Wait, also this...

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You're welcome. Good luck on your quiz!

- OLIVIA B. DARANY