Chapter 13 8th Grade

1
Chapter 138th Grade

• McDowell

2
Polynomials 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
6

• Plug and Chug

Evaluating 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
8
Adding 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
11
Subtraction
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
12
Vertical Method
(-4x² x 1) (x² - x 8)

• Change, Change, Go

(-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