4.4 and 4.5
Can you see the end?
2 common mishaps
 2(3-4x+2) What do I do first? Distribute?
 x-4(5+2x) = x – 20 – 8x Parenthesis go
away
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
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!
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)
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
Tricky things
 Evaluate: 5-2/5
 (3ab-4)(-2a-3b7)
 [6m2n3/8m7n2]-3
27/64
 4a-2b5/6a5b2
Note: 6*6*6 =216 and 8*8*8 = 512 and 216/512 =
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
 0.0000832
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
You Try It
 (-2x2)(x-3y-4)-2
 (6a-2b3)-1/(4a3b-2)-2
 [6r3s-3/9r3s-1]-2
 Write 0.000000961 in scientific notation now!
 Write the number 7.329 x 106 in decimal
notation
Answers
 -2x8y8
 8a8/3b7
 9s4/4
 9.61x10-7
 7,329,000
Homework for 4.4
 Section 4.4 HW
 1-123 every other odd
 2, 8, 20, 36, 60, 74, 92, 104, 110, 118,
128
Section 4.5 – Division of
Polynomials
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
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
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)
Now You do it
 (2x3 +x2 -8x -3) / (2x-3)
 (x3 – 2x +1)/ (x-1)
Soln’s
 X2 + 2x -1 – 6/(2x-3)
 X2 +x -1
homework
 Section 4.5 HW
 1-55 eoo
 2, 12, 20, 32, 40, 50