1. 4.4 and 4.5
Can you see the end?

2. 2 common mishaps 2(3-4x+2) What do I do first? Distribute?
x-4(5+2x) = x – 20 – 8x Parenthesis go away

3. Exponents & Scientific Notation
Dividing Monomials
Note: When you multiply monomials, you add the exponents.
When you divide monomials, you subtract the exponents!!!!!!
x5/x2
a7/a3
(r8*t6)/(r7t)
p7/z4

4. Those crazy zeros x4/x4 (12a3)0 where a doesn’t equal 0 -(4x3y7)0
Note: a variable in the denominator cannot equal zero because that would make the problem undefined!

5. The negative Exponent Def1: x-n = 1/xn Def2: 1/x-n = xn x4/x6
Evaluate and Simplify
2-4
3n-5
2/(5a-4)

6. Exponents + Fractions = Mess
If you have a fraction and it has an exponent, multiply each exponent in the quotient by the outside exponent
(a3/b2)4
Negative Exponent
Method 1 (same as above)
(x2/y3)-2
Method 2 (do the reciprocal)
(t4/r2)-3

7. Tricky things Evaluate: 5-2/5 (3ab-4)(-2a-3b7)
[6m2n3/8m7n2]-3 Note: 6*6*6 =216 and 8*8*8 = 512 and 216/512 = 27/64
4a-2b5/6a5b2

8. Scientific Notation
How to write really really big numbers or really really small numbers
Usually used in the natural sciences.
Big numbers – Distances in Space, electrical forces like volts, my ego.
240,000
93,000,000
Small numbers – Microscopic Things, Biology, Chemistry.
0.0003

9. Going the other way Positive exponents 3.45 x 106 2.3 x 108
Negative exponents
8.1 x 10-3
6.34 x 10-7

10. You Try It (-2x2)(x-3y-4)-2 (6a-2b3)-1/(4a3b-2)-2 [6r3s-3/9r3s-1]-2
Write in scientific notation now!
Write the number x 106 in decimal notation

11. Answers
-2x8y8
8a8/3b7
9s4/4
9.61x10-7
7,329,000

12. Homework for 4.4 Section 4.4 HW 1-123 every other odd
2, 8, 20, 36, 60, 74, 92, 104, 110, 118, 128

13. Section 4.5 – Division of Polynomials

14. Divide Divide Divide! Polynomial by a monomial
It’s the opposite of distribution
Let me show you how:
(6x3 – 3x2 +9x) / 3x
Have another
(12x2y – 6xy + 4x2) / 2xy

15. Divide by polynomials Long division…because you love it
(x2-5x+8) / (x-3)
What if a term is missing?
Put a zero in for the missing term
(6x+26-2x3) / (2+x)
Note: remainder gets put over the divisor

16. Check it out How do you check?
All you gots to do is multiply your answer by the divisor and add your remainder.
DON’T FORGET THE REMAINDER!!!!!
Another example:
(x^2-1)/(x+1)

17. Now You do it
(2x3 +x2 -8x -3) / (2x-3)
(x3 – 2x +1)/ (x-1)

18. Soln’s
X2 + 2x -1 – 6/(2x-3)
X2 +x -1

19. homework
Section 4.5 HW
1-55 eoo
2, 12, 20, 32, 40, 50