Any questions on the Section 6 2 homework Now please CLOSE YOUR LAPTOPS and turn off and put away your cell phones Sample Problems Page Link Dr Bruce Johnston Section 6 3 and 6 4 Complex Fractions and Dividing Polynomials Key Concepts from Section 6 3 Complex rational expressions complex fractions are rational expressions whose numerator denominator or both contain one or more rational expressions Example of a complex fraction 10 3x 5 6x Solution view as a division problem 10 5 10 6x 4 3x 6x 3x 5 Problem from today s homework Problem from today s homework Note This one requires that you first combine the added or subtracted pairs of rational expressions into single rational expressions with a common denominator Section 6 4 Dividing a polynomial by a monomial Divide each term of the polynomial separately by the monomial Example 12a 3 36a 15 12a 3 36a 15 3a 3a 3a 3a 5 2 4a 12 a Problem from today s homework Dividing a polynomial by a polynomial other than a monomial uses a long division technique that is similar to the process known as long division in dividing two numbers This process is reviewed in detail on the next slide but first we ll work these two simpler examples on the whiteboard 1 225 9 2 231 9 Question How can you check your answers on long division problems Example Long Division with integers 168 43 7256 43 295 258 37 6 344 32 Divide 43 into 72 Multiply 1 times 43 Subtract 43 from 72 Bring down 5 Divide 43 into 295 Multiply 6 times 43 Subtract 258 from 295 Bring down 6 Divide 43 into 376 Multiply 8 times 43 Subtract 344 from 376 Nothing to bring down 32 We then write our result as 168 43 As you can see from the previous example there is a pattern in the long division technique Divide Multiply Subtract Bring down Then repeat these steps until you can t bring down or divide any longer We will incorporate this same repeated technique with dividing polynomials Now you try it And don t forget to check your answer Divide 3471 by 6 using long division Then check your answer Do this in your notebook now and make sure you ask if you have questions about any step This will be crucial to your understanding of long division of polynomials Example with polynomials 4x 5 2 7 x 3 28 x 23x 15 2 28 x 12 x 35 x 15 35 x 15 Divide 7x into 28x2 Multiply 4x times 7x 3 Subtract 28x2 12x from 28x2 23x Bring down 15 Divide 7x into 35x Multiply 5 times 7x 3 Subtract 35x 15 from 35x 15 Nothing to bring down So our answer is 4x 5 Check Multiply 7x 3 4x 5 and see if you get 28x2 23x 15 Now you try it And don t forget to check your answer Divide 6x2 x 2 by 3x 2 division Then check your answer using long Do this in your notebook now and make sure to ask if you have questions about any step ANSWER 2x 1 Example 2 x 10 2 2 x 7 4x 6 x 8 2 4 x 14 x 20x 8 20x 70 78 Divide 2x into 4x2 Multiply 2x times 2x 7 Subtract 4x2 14x from 4x2 6x Bring down 8 Divide 2x into 20x Multiply 10 times 2x 7 Subtract 20x 70 from 20x 8 Nothing to bring down We write our final answer as 2 x 10 78 2 x 7 How do we check this answer 2 x 10 2 2 x 7 4x 6 x 8 2 4 x 14 x 20x 8 20x 70 78 Final answer 2x 10 78 2x 7 How to check Calculate 2x 7 2x 10 78 If it comes out to 4x2 6x 8 then the answer is correct Now you try it And don t forget to check your answer Divide 15x2 19x 2 by 3x 5 using long division Then check your answer Do this in your notebook now and make sure you ask if you have questions about any step Answer 5x 2 8 3x 5 Problem from today s homework Problem from today s homework Something to be aware of on Problem 14 in today s homework The online Help Me Solve This instructions for this problem demonstrate a method called Synthetic Division We are not covering this method in class because it is only useful in the cases where the divisor is of the form x c You will get the same answer using the long division method so this is what we expect you to use to solve this problem If you are already familiar with synthetic division you re welcome to use it in those cases where it is applicable but we aren t expecting you to learn it on your own Reminder This homework assignment on section 6 4 and 6 3 is due at the start of next class period You may now OPEN your LAPTOPS and begin working on the homework assignment