Title: Chapter 13 8th Grade
1Chapter 138th Grade
2Polynomials 5/5
monomial
- A real number, a variable, or a product and a
real number and variable with whole number
exponents
An expression without addition,
subtraction---cant divide by a variable
Examples
monomial
Not a monomial
5 xy/2 -112a 3m³n²
7 - a xy/z 34 b 4k-³
3- Is the expression a monomial?
- 5 c
- 7z/3
- 6ab²
- 4g/h
- -0.3y
- 7
You try
No Yes Yes No Yes Yes
4- A monomial or the sum or difference of monomial(s)
polynomial
term
The monomials that make up a polynomial
Polynomial of terms Example
Monomial 1 h, 3d/4, ¼p³
Binomial 2 w 4, 3f r²
Trinomial 3 x² 5x 23
Polynomial 1 or more All of the above
5- Name the polynomial
- 5c 2 a
- 56 x
- 21
- 3x² 2x
- 7p²
- ab a b
You try
Trinomial Binomial Monomial Binomial Monomial trin
omial
6Evaluating polynomials
Evaluate the 3x for x 5
3x
Plug in the values
3(5)
Chug out the answer following PEMDASLR
15
Evaluate gh³ 4g - ½h for g 10, h 4
gh³ 4g - ½h
Plug in the values
(10)(4)³ 4(10) - ½(4)
Chug out the answer following PEMDASLR
(10)(64) 4(10) - ½(4)
640 40 - 2
680 - 2
672
7- Evaluate the expression for a 2, b -4
- 10a b² - 7
- -4ab
- a² - 2b - 3
- a - 3b
- ab² 5
- 2a
You try
8Adding and Subtracting Polynomials 5/6
- Like terms have the same variable and exponent or
no variable at all
Like terms
Vertical Method
Find like terms
(4b² 2b 1) (7b² b 3)
Add like terms
11b² b - 2
9- (2y² - 9y 15) (6y² 8y 11)
Vertical Method
Line up like terms
2y² - 9y 15 6y² 8y 11
Combine like terms
2y² - 9y 15 6y² 8y 11
8y²
- 1y
- 26
10- Simplify each sum using any method
- (x² 3x 1) (x² x 6)
- (5x² 3x 7) (7x 2)
- x4 3x³ - x² x 2
- 7x³ x² - 5x 9
- xy 5x 2y 4
- 2xy 3x 3y - 8
You Try
11Subtraction
Change subtraction to addition Change the sign of
the 2nd number
- Remember the distributive property
A negative outside parenthesis belongs to
everything inside the parenthesis
12Vertical Method
(-4x² x 1) (x² - x 8)
(-4x² x 1) (x² - x 8)
Distribute the negative sign
(-4x² x 1) (-x² x - 8)
Find like terms
(-4x² x 1) (-x² x - 8)
Combine like terms
-5x² 2x - 9
13 x² - 3x 9 -- 5x - 4
Vertical Method
Change, Change, Go
Distribute the negative sign
x² - 3x 9 -5x 4
x² - 3x 9 -5x 4
Combine like terms
x² - 8x - 5
14- Find the difference
- (ab 4) (3ab 6)
- (2x² 3x 7) (x² - 6x 9)
- 3x² x 7
- - 2x² x 2
- 6y 8
- - 2y 7