<ul><li>-Multiplying and Dividing Monomials </li></ul><ul><li>-Adding and Subtracting Polynomials </li></ul><ul><li>-Multiplying Monomials and Polynomials </li></ul><ul><li>-Multiplying Polynomials </li></ul><ul><li>-Factoring Trinomials of the Form x 2 + bx + c </li></ul><ul><li>-Factoring Trinomials of the Form ax 2 + bx + c </li></ul><ul><li>-Factoring a Difference of Squares </li></ul><ul><li>-Dividing a Polynomial by a Binomial </li></ul>
Multiplying and Dividing Monomials <ul><li>The Coefficient is the number in front of the variable. </li></ul><ul><li>The Constant is the number by itself. </li></ul>Polynomials Monomial x 2x Trinomial s 5a+8b+5c lmn+6+hij Binomials a+7 3a+4b 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.
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: 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. The exponent of x plus the exponent of y would equal 7… Therefore the degree would be 7 since it’s the highest sum. Degree Of A Polynomial 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.
Adding and Subtracting Polynomials Adding and Subtracting Polynomials- To add or subtract polynomials, simply combine like terms. Ex: 14 x 4 y +11 x 4 y +3 xy 5 +2 xy 5 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.
Multiplying Monomails and Polynomials Multiply 2x with 2x and multiply 2x with –2y. Multiply 3 with everything inside the brackets… Factor to check if you have the right answer. Distributive Property Ex: 2x(2x-2)-(-2x+4) Multiply everything in the brackets with -1 2x(2x-2)+2x-4 Multiply 2x with (2x-2) 4x 2 -4x+2x-4 Combine like terms 2x 2 -2x-4
Ex: Expand: Step 1: Multiply the coefficients and the constant terms. Common Mistakes: Remember to multiply ALL coefficients and constant terms. Never forget the negative sign, and variables too. Step 2: Combine like terms.
Quadratic Term Linear Term Constant Term Ex: Find the common factor, and remove it first. 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. Factoring Trinomials of the Form x2+bx+c First, find two integers that have a product of 6 and a sum of 5.
Ex: Find two integers with the sum of 18 and a product of 8 and –5. Ex: Factor Common Mistakes: Don’t forget to bring out the common factor first. Factoring Trinomials of the Form ax2+bx+c 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.
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. Factoring A Difference Of Squares
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
Change the sign of 2x and 2y. Combine like terms Then, combine like terms
Multiply 4x with everything in the brackets Find a common factor
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.
Find the square root of 255 First, find a common factor. It would be 2 Find the square root of both numbers
Bring everything to one side Factor… Then solve… Therefore… Bring everything to one side Factor… Then solve…
Find a number to multiply by x-2 to get x 3 -5x 2 x 2 Multiply x 2 with x-2 x 3 -2x 2 Subtract x 3 -2x 2 from x 3 -2x 2 and bring down the –x. -3x 2 -x Find another number and multiply again -3x 2 +6x -3x Subtract and bring down the -10 -7x-10 Again, find a number that goes into -7x-10 and then multiply again -7 Subtract and find to remainder -7x+14 -24 R-24 First add a 0a 2 in between the a 3 and –19a Find a number that goes into a 3 + 0a 2 . It would be a 2 a 2 Multiply, subtract, and bring down the 19a a 3 -3a 2 3a 2 -19a Find a number that goes into 3a 2 -19a +3a 3a 2 -9a Subtract and bring down the –24. -10a-24 Find a number that goes into –28a-24, multiply, subtract and get your remainder. -10 -10a+30 -54 R-54