Polynomial consists 1 or more terms
Classification of a Polynomial
Use distributive property to expand
Distributive property is applied
Concrete Material can be used to model

Polynomials and Equations

Equation is a statement that say 2 expressions are equal. Ex: 3x+3=2x-1

Solution or root of an equation is the value of the variable that makes an equation true.

Solution or root of an equation is the value of the variable that makes an equation true.

Simple Equations

To solve one step equation, do opposite operation to isolate the variable. Ex:   x+4=13
                         x +4 -4 = 13

To solve one step equation, do opposite operation to isolate the variable. Ex: x+4=13
x +4 -4 = 13 -4
x=9

To solve a 2 step equation, either add or subtract to isolate the variable term. Then divide by the coefficient of the variab

To solve a 2 step equation, either add or subtract to isolate the variable term. Then divide by the coefficient of the variable term. Ex: 2x -7 = 9
2x -7 +7 = 9 +7
2x = 16
2x/2 = 16/2
x=8
Keep in mind that you are using SAMDEB

You can also do a check: L.S. = 2(8) - 7         R.S. = 9
                                                   =16 - 7

You can also do a check: L.S. = 2(8) - 7 R.S. = 9
=16 - 7
= 9
L.S. = R.S.

Multi-Step Equations

Multi-Step Equations

To solve an equation with Multiple Terms, collect variable terms one side and constant* terms on the other by doing opposite operation. Ex: 3x +2 = 2x -4
3x +2 -2x = 2x -4 -2x
x +2 = -4
x +2 -2 = -4 -2
x = -6

To solve equations with brackets, you need to expand them. 5 (y-3) - (y-2) = 19
           5 (y-3) - (y-2) = 19
            5

To solve equations with brackets, you need to expand them. 5 (y-3) - (y-2) = 19
5 (y-3) - (y-2) = 19
5y - 15 - y +2 = 19
4y - 13 = 19
4y - 13 + 13 = 19
4y = 32
4y/4 = 32/4
y=8

Check: L.S.= 5 (y-3) - (y-2)              R.S.= 19
                    =5y - 15 - y +2
                    = 5 (8) - 15 - (8)

Check: L.S.= 5 (y-3) - (y-2) R.S.= 19
=5y - 15 - y +2
= 5 (8) - 15 - (8) + 2
=40 -15 -6
= 19
L.S.= R.S.

Equations with fractions

Equations with fractions

Eliminate the fraction by multiplying both side of the equation by the denominator.

6 = ⅓ (8+x)
3 ✕ 6 = 3 ✕ ⅓ (8+x)
18 = 8 + x
18 - 8 = 8 + x - 8
10 = x

For more than one fraction, find the LCD and multiply all the terms on both sides of equation by this value.

k + 2/3 = k - 4/ 5
15 ✕ k + 2/3 = 15 ✕k - 4/ 5
5 (k+2) = 3 (k-4)
5k + 10 = 3k - 12
5k + 10 - 3k - 10 = 3k - 12 - 3k - 10
2k = - 22
2k/2 = - 22/2
k = - 11

Modelling with Formulas

Modelling with Formulas

Algebraic relationship between two or more variables.

To rearrange, isolate the term that contains the variable, and then isolate the variable.

1 step: d = a + b
d - b = a + b - b
d - b = a
Or a = d - b

More then 1 step: y = mx + b
y - b = mx + b - b
y - b = mx
y - b/m = mx/m
y - b/m = x
Or x = y - b/m

Modelling with Algebra

It is a representation of a pattern of numbers.

Example: Alexa works at a record shop. She earns $!0.70/hr plus $0.88 for each album she sells. To model this situation we ca

Example: Alexa works at a record shop. She earns $!0.70/hr plus $0.88 for each album she sells. To model this situation we can say, "h " is the number of hours worked and "a" is the number of albums sold. The expression would be 10.70 h + 0.88 a

Expression VS Equation

Does not have an equal sign
Can't remove fraction (only expand)
We can only simplify

Does not have an equal sign
Can't remove fraction (only expand)
We can only simplify

Has an equal sign
Fractions can be removed (by finding LCD)
We can solve

Has an equal sign
Fractions can be removed (by finding LCD)
We can solve

Polynomial

Polynomial

Made up of term(s) connected by addition or subtraction
operators.

Made up of term(s) connected by addition or subtraction
operators.

To add, remove bracket, collect like terms: (2p-2)+(4p-7)
= 2p-2+4p-7
= 2p+4p-2-7
=  6p-9

To add, remove bracket, collect like terms: (2p-2)+(4p-7)
= 2p-2+4p-7
= 2p+4p-2-7
= 6p-9

To subtract, add its opposite:  (3y+5)-(7y-4)
=(3y+5)+(-7y+4)
=3y+5-7y+4
=3y-7y+5+4
=-4y+9

To subtract, add its opposite: (3y+5)-(7y-4)
=(3y+5)+(-7y+4)
=3y+5-7y+4
=3y-7y+5+4
=-4y+9

Monomial

- 2a3b

Binomial

a3 - b3

Trinomial

x2 - 4x + 4

degree of a Polynomial

highest degree term

5x² - 7x = 2

Term

Like terms

Like terms

identical variables with same exponents on each variable

Add: 4x+ 3x
= 7x

Add: 4x+ 3x
= 7x

Subtract: 8x-3x
=5x

Subtract: 8x-3x
=5x

degree of a term

2/3xy= 1+1=2

Sum of exponents

Sum of exponents

4x²

Varriable= x²

Coefficient= 4

distributive property

Simplifies complicated expressions

Simplifies complicated expressions

Example:

Example:

Subtopic

Algebraic expression

Number, variables, operators

7x+3

Modelling Tiles

Modelling Tiles

Variable

w

w

Ex. 7×7×7=7³

Exponent= ³

base=7

Exponent Laws

Exponent Laws

Product Rule

Ex. xᵃ×xᵇ= xᵃ⁺

Quotient Rule

Ex. xᵃ÷xᵇ= xᵃ⁻ᵇ

Power of Power Rule

Ex. (xᵃ)ᵇ= xᵃˣᵇ