- Measurement Formulas and Monomials - Multiplying and Dividing Monomials

2. -Measurement Formulas and Monomials -Multiplying and Dividing Monomials -Adding and Subtracting Polynomials -Multiplying Monomials and Polynomials -Multiplying Polynomials -Factoring Trinomials of the Form x2+bx+c -Factoring Trinomials of the Form ax2+bx+c -Factoring a Difference of Squares -Solving Quadratic Equations -Dividing a Polynomial by a Binomial

3. Measurement formulas are mostly made of monomials. Monomials are the product of a coefficient and one or more variables. In order to solve the monomial you must substitute a number for each variable. Cylinder: Surface Area: Volume: Sphere: Surface Area: Volume: Height Radius Radius Cube Surface Area: Volume:

4. Multiplying and Dividing Monomials Polynomials Trinomials5a+8b+5c lmn+6+hij Monomial x 2x Binomials a+7 3a+4b The Coefficient is the number in front of the variable. The Constant is the number by itself. Multiplying Add the exponents and Multiply the Coefficients… so the answer would be… Dividing Subtract the exponents and divide the coefficients… so the answer would be… Common Mistakes: Remember to multiply or divide the negative or positive sign of the coefficient in. When dividing, remember to put answer to the exponent where the larger exponent used to be.

5. Degree Of A Polynomial Degree of a Polynomial- To find the degree of a polynomial, add together the exponents on the variable for each term. The largest number is the degree of the polynomial. Ex: Therefore the degree would be 7 since it’s the highest sum. The exponent of x plus the exponent of y would equal 7… The exponent “4” from the x, plus the exponent “1” from the y would equal 5. The exponent from x plus the exponent of y would equal 2. The exponent of x plus the exponent of y would equal 6. Common Mistakes: When finding the degree, if it’s just a variable by itself, don’t forget to add one even if it doesn’t have a one as an exponent.

6. Adding and Subtracting Polynomials Adding and Subtracting Polynomials- To add or subtract polynomials, simply combine like terms. Ex: 14x4y+11x4y+3xy5+2xy5 These two are like terms These two are like terms… Common Mistakes: Remember to switch the variables for each term when adding or subtracting if they are not in alphabetical order so you won’t forget to add them in the end.

7. Distributive Property Multiplying Monomails and Polynomials Ex: 2x(2x-2)-(-2x+4) Multiply 2x with 2x and multiply 2x with –2y. Multiply everything in the brackets with -1 2x(2x-2)+2x-4 Multiply 3 with everything inside the brackets… Multiply 2x with (2x-2) 4x2-4x+2x-4 Factor to check if you have the right answer. Combine like terms 2x2-2x-4

8. Ex: Expand: Step 1: Multiply the coefficients and the constant terms. Step 2: Combine like terms. Common Mistakes: Remember to multiply ALL coefficients and constant terms. Never forget the negative sign, and variables too.

9. Factoring Trinomials of the Form x2+bx+c Quadratic Term Linear Term Constant Term Ex: Find the common factor, and remove it first. First, find two integers that have a product of 6 and a sum of 5. Find two integers that have a product of –4 and a sum of 3. Common Mistakes- If there is a negative sign, don’t forget about it and make sure you use it when factoring. Another common mistake would be forgetting to find the common factor first.

10. Factoring Trinomials of the Form ax2+bx+c Ex: Find two integers with the sum of 18 and a product of 8 and –5. Ex: Factor Bring out the common factor first Find two integers so that the sum of the product of the inside and outside terms is -11 and they have a product of 5 and 2. Common Mistakes: Don’t forget to bring out the common factor first.

11. Factoring A Difference Of Squares Find the square root of 16. One is negative and one positive. Then, factor. Common Mistakes: When factoring a binomial, don’t forget to remove the common factor first.

12. Quadratic Equations: Common Mistakes- Don’t forget to bring out the common factor first if you can.

13. Dividing a polynomial by a binomial is just like long division. It has a divisor, quotient, remainder and dividend just like long division. Ex: When dividing, always look at the first term. You multiply 3x with x to get 3x2, or you can take 3x2 and divide it by x to get 3x. Then you multiply 3x by 2 to get 6x. And don’t worry about the second one. Bring down the 11. Then subtract 6x from 8x to get 2x. Take 2x and divide it by x to get 2 Subtract 4 from 11 to get 7 as a remainder.

14. Diameter is 3.8cm 5.5cm 3. Simplify 4. Simplify 5. Simplify 6. Simplify

15. Answers

16. Diameter is 3.8cm 5.5cm

17. Multiply the coefficients Add the exponents of like terms Multiply coefficients and add the exponents of like terms Subtract the exponents of like terms and divide the coefficients

18. Combine like terms Change the sign of 2x and 2y. Then, combine like terms

19. Multiply 4x with everything in the brackets Find a common factor

21. Find two integers with the product of 9 and sum of 6. Find 2 integers with the product of 72 and the sum of 17.

23. Find the square root of 255 First, find a common factor. It would be 2 Find the square root of both numbers

24. Bring everything to one side Factor… Then solve… Therefore… Bring everything to one side Factor… Then solve…

25. Find a number to multiply by x-2 to get x3-5x2 x2 -3x -7 R-24 Multiply x2 with x-2 Subtract x3-2x2 from x3-2x2 and bring down the –x. x3-2x2 Find another number and multiply again -3x2-x Subtract and bring down the -10 -3x2+6x Again, find a number that goes into -7x-10 and then multiply again -7x-10 -7x+14 Subtract and find to remainder -24 First add a 0a2 in between the a3 and –19a Find a number that goes into a3+ 0a2. It would be a2 a2 +3a -10 R-54 Multiply, subtract, and bring down the 19a Find a number that goes into 3a2-19a a3-3a2 Subtract and bring down the –24. 3a2-19a 3a2-9a Find a number that goes into –28a-24, multiply, subtract and get your remainder. -10a-24 -10a+30 -54