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ALGEBRA - Coggle Diagram
ALGEBRA
4.2: Adding and Subtracting Polynomials (pgs: 143-147)
Polynomials
: sum of
monomials
Monomials
: An
expression
that is either
numeral
, a
variable
, or a
product of a numeral
and one or more variables.
7
h
1/2
c
Degree of a Monomial
: Is the
total number
of times its variables occurs as factors
-3
xy
2
z
3
1 in x
2 in y
3 in z
Binomials
: two terms
4
x
+ 9
Trinomial
: three terms
5
b
+ 3
ab
+
a
coefficient
: The number at the side of a variable
8
a
Degree of a Polynomial
: Is the greatest of the degrees of its terms after it has been simplified
Subtracting
Polynomials
is very much like subtracting real numbers. To subtract a number you add the opposite of that number. To subtract a
polynomial
you add the opposite of each term of the polynomial that you are subtracting and then simplify.
Whenever you add a polynomial, you add first the coefficients and then the variable with its exponent stays the same (exponents are
NOT
added)
Like Terms
: Two monomials that are exactly alike
-4
x
+ 5
x
Here the
x
is the like term
In an equation, only like terms can be added/subtracted/multiplied/divided
4.1: Exponents
(pgs: 136-142)
The exponent indicates the number of times the base occurs as a factor
exponential form
2 cubed
factored form
2 x 2 x 2
In order to solve an expression/formula with exponents you have to follow the
Order of Operations
PEMDAS: P
arenthesis
E
xponents
M
ultiplication
D
ivision
A
dditon
S
ubtraction
4.3: Multiplying Monomials (pgs: 148-150)
When you're multiplying
monomials
and you have two powers with the same base, you add the
exponents
x
2 +
x
8 =
x
(2+8) =
x
10
4.5: Multiplying a Polynomial by a Monomial (pgs: 154-156)
When you're multiplying a
Polynomial
by a
Monomial
you need to use
Distributive Property
and multiply the monomial by all the monomials into the polynomial
Distributive Property
: To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more
polynomials
by a number(
monomial
) will give the same result as multiplying each
polynomial
individually by the number(
monomial
) and then adding the products together.
5(
a
+ 2) = (5 x
a
) + (5 x 2 ) = 5
a
+ 10 = 15
a
4.6: Multiplying Two Polynomials (pgs: 157-160)
When multiplying two
polynomials
you have to do the same as when adding a
monomial
by a
polynomial
. All you have to use is
distributive property
(4
x
+ 3)
(3
x
+ 4)
= 4
x**
(3
x
+ 4)
+ 3
(3
x
+ 4)
* = 12
x
2 + 16
x
+ 9
x
+ 12 = 12
x
2 + 25
x* + 12
Remember that the final answer keeps being an expression since they're NOT like terms
4.4: Powers of Monomials (pgs: 151-153)