Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 8 - Polynomials and Factoring - Coggle Diagram
Chapter 8 - Polynomials and Factoring
Adding and Subtracting Polynomials
Adding and Subtracting them
Simpify
Classifying Polynomials
Classifying Degree
Polynomial (2+)
Find the biggest exponent
Monomial (1)
Add all the exponenets up
Classifying number of terms
2 = Binomial
3 = Trinomial
1 = Monomial
4+ = Polynomial
Multiplying and Factoring
monomial * polynomial
Expand using distributive property
Facotoring monomial and polynomial
Find the GCF and bring factor it out
Vocabularies
Degree of a monomial: the sum of all the exponents in a monomial
Standard form of a polynomial: terms placed in order by exponents (biggest to smallest)
Trinomial: 3 term
Binomial: 2 term
Monomial: 1 term
Multipling Binomials
Special cases
(a-b)(a-b) = a^2 - 2ab + b^2
a^2 - b^2 = (a-b)(a+b)
(a+b)(a+b) = a^2 + 2ab + b^2
FOIL (First outside inside last)
distributing both of the tersm in 1 perenthesis to the other 2 terms in the other perenthesis
Table
Using table, you will have to write every variable 1 by one, put them into a chart, and multiply them up.
Distributive property
Replacing: a parenthesis with a varialble, and replace it back after the replacing variable is distributed
Factoring Polynomials
Step 1: If there is a GCF, factor
Step 2: Use trail and error (it can only be used in the form of ax^2 + bx + c
Trail and error
Step 2: Write bx at the right bottom of the chart
Step 3: Use whatever combination of multiping thta make it possible if we added/subtracted these two numbers to bx
Step 1: write out any 2 terms that multiplies up to ax^2
Step 4: write it in the form of (x+[number you found out worked for c
ax])(x+[number you found out worked for c
ax])
Factoring Polynomials 2
Perfect square (Trinomials)
Step 1: Check if all terms are in the form of a perfect square
Step 2: Check if the middle term can be turned into the for of x
y
z
Step 3: if its orignially ax^2 + bx + c. Turn it into (a+b)^2
Different between 2 squares
Steo 1: check if its in the form of any special cases
Step 2: If it is, turn it back into its orginal state in the special case
Grouping (polynomial(4))
Step 1: find a possible GCF that works in pairs of the terms
Step 2: place the 2 coefficient of the factors into another perenthesis
it should look like this (
+/-
) (
+/-
)
