When you multiply like bases you add the exponents. When you divide like bases you subtract the exponents.

A non-zero base to the power of 0 = 1. A power to a power, multiply the powers.

Simplify by using all exponential properties and positive exponents.

Negative exponents moves the base from the top to the bottom or bottom to the top. Write using positive exponents. Simplify, if possible.

Use exponent properties and write using positive exponents. Simplify, if possible.

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.

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.

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

The sum of the powers on the variables in one term = 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

Write the polynomial in descending order.

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!

Combine Like Terms! Notice that the polynomials are written in descending order! This will make C.L.T. much easier!

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 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.

Distributive Property Multiply like parts. Re-group by Comm. Prop of Mult.

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 * 2x”“5 * 5” Do see the SMILE? SMILE?

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.

( )’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.

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 st 1 2 nd 0 deg. The degree of the polynomial is a 6 th degree. Distribute the minus sign!

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 * 2x”“3 * 3” * Dble IT “2x * 3 = 6x Dble IT” ** * Dble IT

3 “GAZINTA” 15, 5 times and subtract exponents.

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.

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.

Polynomial divided by a binomial. In this problem, notice that the x is missing terms. We must put in 0’s 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.

Polynomial divided by a binomial.