Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

Section 5.6A Dividing Polynomials, Part 1

Section 5.6 Part 1 Dividing a polynomial by a monomial: Divide each term of the polynomial separately by the monomial. Example

Problem from today’s homework:. 3y + y – 4y x x 2

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, try these two simpler examples in your notebook (use long division, not your calculator): 1). 225 ÷ 9 (Answer: 25) 2). 232 ÷ 9 (Answer: 25 with a.. remainder of 7, or /9) Question: How can you check your answers on long division problems? (A: Multiply answer times divisor, e.g. 25 * 9 = 225)

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 is smaller than 43, so we are done. We then write our result as 168 Example: Long Division with integers 32 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 3473 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. Answer: (Can also be written as ) 5656

35  x Divide 7x into 28x 2. Multiply 4x times 7x+3. Subtract 28x x from 28x 2 – 23x. Bring down -15. Divide 7x into –35x. Multiply -5 times 7x+3. Subtract –35x–15 from –35x–15. Nothing to bring down. 15  So our answer is 4x – 5. Example with polynomials: Check: Multiply (7x + 3)(4x – 5) and see if you get 28x 2 – 23x - 15.

Divide 6x 2 – x – 2 by 3x – 2 using long division. Then check your answer. Do this in your notebook now. ANSWER: 2x + 1 Check: Multiply (2x + 1)(3x – 2). What do you get? Now you try it (And don’t forget to check your answer!)

 xxx x2 x x  20  x 10  7020  x 78 Divide 2x into 4x 2. Multiply 2x times 2x+7. Subtract 4x x from 4x 2 – 6x. Bring down 8. Divide 2x into –20x. Multiply -10 times 2x+7. Subtract –20x–70 from –20x+8. Nothing to bring down. 8   )72( 78  x x2 10  We write our final answer as Example

 xxx x2 x x  20  x 10  7020  x 78 8  How do we check this answer? Final answer: 2x – x + 7 How to check: Calculate (2x + 7)(2x – 10) If it comes out to 4x 2 – 6x + 8, then the answer is correct.

Now you try it (And don’t forget to check your answer!) Divide 15x x – 2 by 3x + 5 using long division. Then check your answer. Do this in your notebook now. Answer: 5x – x + 5

REMINDERS: The assignment on today’s material (HW 5.6A) is due at the start of the next class session. Open Lab hours in 203: 8:00 a.m. to 7:30 p.m., M-Th Please remember to sign in on the Math 110 clipboard by the front door of the lab

You may now OPEN your LAPTOPS and begin working on the homework assignment. We expect all students to stay in the classroom to work on your homework till the end of the 55- minute class period. If you have already finished the homework assignment for today’s section, you should work ahead on the next one or work on the next practice quiz/test.