02 Adding and Subtracting Polynomials.notebook
February 07, 2014
Middle School Math Review:
3
+ 2
5
3x
+ 2x
5x
3x
2x
+ 3
5x + 3
Middle School Math
Middle School Math Review:
How do you solve:
(2x + 8) + (x - 3)
2x + 8 means
2 x's and
8 ones
x - 3 means
1 x and
"take away" 3 ones
Middle School Math
1
02 Adding and Subtracting Polynomials.notebook
February 07, 2014
Steps for Adding Polynomials
1. Identify like terms
2. Combine coefficients of like terms
a. If signs are the same ADD and take sign of larger
b. If signs are different subtract and take sign of larger
Steps for Adding Examples: Use Algebra Tiles if you'd like
1. (2x2 ­ 5x) + (3x2 + x)
2. (9y ­ 7x) + (8x ­ 3y)
6y + x
5x2 - 4x
x
­x
x2
1
­1
­x2
y
­y
y2
­y2
xy
Examples 1 & 2
2
02 Adding and Subtracting Polynomials.notebook
February 07, 2014
Examples: Use Algebra Tiles if you'd like
3. (x2 ­ 5x + 3) + (4x ­ 3)
4. (3x2+3xy­y2) + (4x+6y2)
x2 - x
3x2 + 4x + 3xy + 5y2
x
­x
x2
1
­1
­x2
y
y2
­y
­y2
xy
Examples 3 & 4
Additive Inverse:
"-a" is the additive inverse of "a" if
a + (-a) = 0
In other words:
a and -a cancel each other out!
Additive Inverse
3
02 Adding and Subtracting Polynomials.notebook
February 07, 2014
State the Additive Inverse of each Polynomial
1. x + 2y
2. 2x2 ­ 3x + 5
-x - 2y
-2x2 + 3x - 5
3. ­8x + 5y ­ 7z
4. 3x3 ­ 2x2 ­ 5x
8x - 5y + 7z
-3x3 + 2x2 + 5x
Additive Inverse Examples
Steps for Subtracting Polynomials
1. Distribute the negative
(change 2nd parenthesis to the additive inverse)
2. Identify like terms
3. Combine coefficients of like terms
a. If signs are the same - ADD and take sign of larger
b. If signs are different -SUBT. and take sign of larger
Steps for Subtracting 4
02 Adding and Subtracting Polynomials.notebook
February 07, 2014
Examples: Use Algebra Tiles if you'd like
1. (7x ­ 11y) ­ (3x + 4y)
2. (5x2­4x+7) ­ (2x2­3x+3)
4x - 15y
x
3x2 - x + 4
­x
1
y
­1
y2
­x2
x2
­y
­y2
xy
Examples 1 & 2
Examples: Use Algebra Tiles if you'd like
3. (4y2 ­ 3y) ­ (6y2 + 5y + 7)
4. 5x2 ­ 4x + 7 ­ 2x2 ­ 3x + 3
-2y2 - 8y - 7
x
3x2 - 7x + 10
­x
x2
1
­1
­x2
y
­y
y2
­y2
xy
Examples 3 & 4
5
02 Adding and Subtracting Polynomials.notebook
February 07, 2014
Set up an algebraic equation and solve
1. The measure of each side of a triangle is 3x + 1. Find its perimeter.
1
+ 3x
Each side is 3x + 1, so...
P = 3(3x + 1)
P = 9x + 3
2. The perimeter of triangle ABC is 7x + 2y. Find the
measure of the third side.
B
Since P = 7x + 2y
& P = AB + BC + AC
2x
+y
3x
-5
y
C
A
7x + 2y = (2x + y) + (3x - 5y) + AC
7x + 2y = 5x - 4y + AC
-5x + 4y -5x + 4y
2x + 6y = AC
Story problems
Homework:
Worksheet 9-2
Quiz Next Class!!
Homework
6