When you multiply like bases you add the exponents. When you
divide like bases you subtract the exponents. Slide 2 A non-zero
base to the power of 0 = 1. A power to a power, multiply the
powers. Slide 3 Simplify by using all exponential properties and
positive exponents. Slide 4 Negative exponents moves the base from
the top to the bottom or bottom to the top. Write using positive
exponents. Simplify, if possible. Slide 5 Use exponent properties
and write using positive exponents. Simplify, if possible. Slide 6
Place the decimal point to create a number between 1 and 10. Count
the number of decimal places, this is the power on 10. Notice that
the power is negative! Exponent sign rule. Original number > 1,
Positive exponent. Original number < 1, Negative exponent. Slide
7 Multiply like bases of 10, add the exponents Multiply the two
decimal numbers. TOO BIG TOO SMALL Change 62.9 to scientific
notation. Divide like bases of 10, subtract the exponents Divide
the two decimal numbers. Change 0.25 to scientific notation. Slide
8 numbervariable ( quantity ) multiplieddivided sumdifference
divided A one term polynomial.3x23x2 7x7x2xyz6 A two term
polynomial.3x 2 + 7x 2xyz 6 A three term polynomial. 3x 2 + 7x 6
Slide 9 The sum of the powers on the variables in one term. 2 + 3 =
5, 5 th degree The term with the highest degree will be the degree
of the polynomial. The value that is multiplied to a variable in a
term. The term with the highest degree will be the leading term of
the polynomial ONLY if the polynomial consists of one variable! The
value that is multiplied to the leading term. Polynomials that
consists of one variable are traditionally written with the powers
on the variable in descending order. This way the leading term is
written first in the polynomial. Below 3x 2 is the leading term, 3
is the leading coefficient, and the polynomial is a 2 nd degree. 3x
2 + 7x 6 Slide 10 Write the polynomial in descending order. Slide
11 powers/exponents Largest powers 1 st ( ) ( )s around every
variable x and the value you want to substitute. Place the -2 into
the ( )s Evaluate each term separately and then combine all the
values. OPPOSITES cancel! Slide 12 Combine Like Terms! Notice that
the polynomials are written in descending order! This will make
C.L.T. much easier! Slide 13 Slide 14 x x r = x Perimeter is the
distance around the object. Fill in the missing outer sides and
find the sum of the outer sides. These are all rectangles so
opposite sides are the same. 3 5 x + x + x + x + 3 + 3 + 5 + 5
Perimeter = 4 x + 16 units Area is the space inside the rectangles.
Find the area of each rectangle. A = L * W x * x = x 2 5x5x 3x3x15
Add each individual area together. x 2 + 5x + 3x + 15 Area = x 2 +
8x + 15 sq. units Area of a circle is The area will be BIG CIRCLE
small circle. r = 5 r is the radius of the circle. Slide 15
Distributive Property Multiply like parts. Re-group by Comm. Prop
of Mult. Slide 16 Double Distributive Property or F.O.I.L. FIOL
x2x2 + 6x 3x 18 F = First terms O = Outer terms I = Inner terms L =
Last terms C. L.T 3x33x3 + 5x 12x 2 20 No like terms x2x2 + 6x 6x
36 Cancels Binomials with the same 1 st terms, but opposite 2 nd
terms are called CONJUGATE PAIRS. The middle terms always cancel. (
a + b ) ( a b ) = a 2 b 2. Just multiply F and L. 4x24x2 9
Binomials that are squared need to written twice and FOILed. The
middle terms are always the SAME. When we combine them, it DOUBLES.
( a + b ) 2 = a 2 + 2ab + b 2 or ( a b ) 2 = a 2 - 2ab + b 2. Mr.
Fitz does the SMILE technique. Do you see a pattern? * Dble IT * *
2x * 5 = 10x Dble IT 2x * 2x5 * 5 Do see the SMILE? SMILE? Slide 17
We will need more arrows. Line up like terms 4x34x3 10x 5x 2 6 3x +
8x 2 C.L.T. No room for more arrows! Try vertical alignment. I
prefer the polynomial with coefficients of 1 on the bottom. Slide
18 ( )s around all variables and the value you want to substitute.
Evaluate each term separately and then combine all the values. ( )
Because the powers are the same, we can move the -2 and 5 into the
( )s and make it -10 which is easier to multiply by! If the
directions want the answer in terms of pi, treat pi like a variable
and leave it in the answer. If the directions want the answer in
decimal form, use and not the symbol on the calculator. The answer
will be to big. Slide 19 Combine like terms. Find the degree of the
terms and the polynomial. Perform the indicated operations. It will
help to keep variables in alphabetical order to better recognize
the same powers on the variables 1 5 th 6 th 1 2 nd 1 1 1 st 1 2 nd
0 deg. The degree of the polynomial is a 6 th degree. Distribute
the minus sign! Slide 20 Perform the indicated operations. 2x22x2 +
10xy 3xy 15y 2 C. L.T If you look close, these two trinomials can
be re-written as a conjugate pair of binomials. * * 2x * 2x3 * 3 *
Dble IT 2x * 3 = 6x Dble IT ** * Dble IT Slide 21 3 GAZINTA 15, 5
times and subtract exponents. Slide 22 Polynomial divided by a
binomial. Old style LONG DIVISION Our goal is to eliminate the
leading term on the inside. Therefore we only divide leading terms.
x2x2 + 3x New leading terms to divide. 2x 2x+ 6 Distribute to the
front terms and line them up under the division box. Line up the x
above 5x. Subtract both columns. Leading terms must CANCEL! Bring
down the next term and repeat. Line up the 2 above 6 as + 2.
Distribute to the front terms and line them up under the division
box. Subtract both columns. Slide 23 Polynomial divided by a
binomial. Our goal is to eliminate the leading term on the inside.
Therefore we only divide leading terms. 2x22x2 1x New leading terms
to divide. 6x 6x 3 Distribute to the front terms and line them up
under the division box. Line up the x above 5x. Subtract both
columns. Fix double signs. Leading terms must CANCEL! Bring down
the next term and repeat. Line up the 3 above 1 as + 3. Distribute
to the front terms and line them up under the division box.
Subtract both columns. We have a remainder. We will add it to the
answer as plus a fraction. Slide 24 Polynomial divided by a
binomial. In this problem, notice that the x 3 + 1 is missing
terms. We must put in 0s to hold the place value of the terms so we
can line them up when subtracting. Divide leading terms. x3x3 + 1x
2 New leading terms to divide. 1x 2 1x Distribute to the front
terms and line them up under the division box. Line up the x 2
above 0x 2. Subtract both columns. Leading terms must CANCEL! Bring
down the next term and repeat. Line up the 1x above 0x. Distribute
to the front terms and line them up under the division box.
Subtract both columns. Bring down the next term and repeat. Slide
25 Polynomial divided by a binomial.
