1. Warm Up W1D5 8/10/11 2. Solve: |4x+2|=5 8x-4 1. = 30 2 3. 5|x+2|=15
= 30 2
3. 5|x+2|=15
4. -5 ≤ 4u-6 ≤ 14
5. Simplify x2x=

2. Adding, Subtracting, Multiplying, and Dividing Polynomials
August 10, 2011
Week 1 Day 5
EQ: How do we add, subtract, multiply, and divide polynomials?

3. Adding Polynomials Simplify: (2x+5y)+(3x-2y) 2x+5y+3x-2y 2x+3x+5y-2y
Combining Like Terms and following Order of Operations (PEMDAS)

4. You Try! Simplify (3x3+3x2-4x+5)+(x3-2x2+x-4)
Did you get 4x3+x2-3x+1?

5. You Try! Simplify (x3+5x2-2x)+(x3+3x-6)+(-2x2+x-2)
Did you get 2x3+3x2+2x-8?

6. Subtracting Polynomials
Simplify:
(x3+3x2+5x-4)-(3x3-8x2-5x+6)
X3+3x2+5x-4-3x3+8x2+5x-6
X3-3x3+3x2+8x2+5x+5x-4-6
-2x3+11x2+10x-10
Just like adding.
Just remember:
Distribute the negative!

7. You Try! Simplify (6x3-2x2+8x)-(4x3-11x+10)
Did you get
2x3-2x2+19x-10?

8. BEFORE we multiply polynomials:
Remember Rules of Exponents?
Multiplying: ( x4)(x3)
= (xxxx)(xxx)
=xxxxxxx
=x7
When we multiplying two numbers with the same base, we add our exponents.
(x4)(x3)
=x(4+3)
=x7

9. Multiplying Polynomials
Simplify:
-3x(4x2-x+10)
-3x(4x2)-3x(-x)-3x(10)
-12x3+3x2-30x
When multiplying one term by a multi-term polynomial,
DISTRIBUTE!

10. You Try! Simplify 4x2 (4x3-x+8)
Did you get
16x5-4x3+32x2?

11. Multiplying Polynomials
Simplify:
(x+3)(x+2)
x2+5x+6
When multiplying a two-term polynomial by a two-term polynomial, we
FOIL or BOX! x2 2x 3x 6

12. You Try! Simplify (4x3-x)(x+8)
Did you get 4x4+32x3-x2-8x?

13. Multiplying Polynomials
Multiplying multi-term polynomial by another multi-term polynomial, it is similar to the FOIL method and distributing
Simplify:
(4x2-4x-7)(x+3)
4x3-4x2-7x+12x2-12x-21
4x3-4x2+12x2-7x-12x-21
4x3-+8x2-19x-21

14. You Try! Simplify (x+2)(x3+3x2+4x-17)
Did you get x4+5x3+10x2-9x-34?

15. When dividing a polynomial by another polynomial, we
Dividing Polynomials X2
- 2x
+ 4
When dividing a polynomial by another polynomial, we
LONG DIVISION!
3x x3-5x2+10x+4
3x3-x2
+10x+4
-6x2 - 2x +4
12x+4
-6x2
12x

16. Together, let’s try to divide (4x4+3x3+2x+1) by (x2+x+2)
We get 4x2-x-7+
x2+x+2

17. You try to divide (2x3-9x2+25) by (2x-5)
Did you get x2-2x-5?

18. Applying to Other Applications
What is the perimeter of the triangle?
x2+5x+1
4x2+2x-7
7x2-2

19. Applying to Other Applications
What is the area of the parallelogram?
2x2-7
3x2+x-5

20. Wrap Up What did we do today?
When multiplying two terms with the same base, what do we do with the exponents?
What is a method we use when multiplying two two-term polynomials?
Add, Subtract, Multiply, and Divide Polynomials
Multiply the exponents
FOIL or BOX method

21. Worksheet: Adding, Subtracting, Multiplying, and Dividing Polynomials
Homework
Worksheet: Adding, Subtracting, Multiplying, and Dividing Polynomials
Add/Subtract: #1-11 odd, 13a, 14, 15
Multiply/Divide: #2-16 even, all, 28a