Entry Task – No calculators

Chapter 5.4 Dividing Polynomials Target: I know how to divide polynomials using long division. I know how to divide using synthetic division (Day 2)

Divide x 2 – 9x – 10 by x + 1 First, I set up the division: For the moment, I'll ignore the other terms and look just at the leading x of the divisor and the leading x 2 of the dividend If I divide the leading x 2 inside by the leading x in front, what would I get? I'd get an x. So I'll put an x on top: Now I'll take that x, and multiply it through the divisor, x + 1. First, I multiply the x (on top) by the x (on the "side"), and carry the x 2 underneath: Then I'll multiply the x (on top) by the 1 (on the "side"), and carry the 1x underneath: Then I'll draw the "equals" bar, so I can do the subtraction. To subtract the polynomials, I change all the signs in the second line...subtract

...and then I add down. The first term (the x 2 ) will cancel out: Now I look at the x from the divisor and the new leading term, the –10x, in the bottom line of the division. If I divide the –10x by the x, I would end up with a –10, so I'll put that on top: I need to remember to carry down that last term, the "subtract ten", from the dividend:

Now I'll multiply the –10 (on top) by the leading x (on the "side"), and carry the –10x to the bottom: and I'll multiply the –10 (on top) by the 1 (on the "side"), and carry the –10 to the bottom: I draw the equals bar, and change the signs on all the terms in the bottom row: Then I add down: Then the solution to this division is: x – 10

3x x

Is 2x -3 a factor of Try this one, then click net and check your work.

Things to think about…. 1) If there is a remainder, the divisor is not a factor 2) There are tons of examples online. Google “dividing polynomials” look at pictures or videos. 3) Also don’t forget the online book and the online tutoring. 4) It is vital you can do regular long division. Practice the entry Task! 5) Here is a website that may answer questions – Click Here Click Here

Assignment Pg 308 #9-18

Day 2 - Synthetic Entry Task Is x+2 a factor of 3x x 2 –x - 12

Synthetic Division Summary 1.Set denominator = 0 and solve (box number) 2.Bring down first number 3.Multiply by box number and add until finished 4.Remainder goes over divisor or as “r” (remainder) Notes of Caution 1.ALL terms must be represented (even if coefficient is 0) 2.If box number is a fraction, must divide final answer by the denominator To evaluate a function at a particular value, you may EITHER: A)Substitute the value and simplify OR B)Complete synthetic division…the remainder is your answer

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Homework P. 308 #32-39 and Challenge #64

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