anonymous
  • anonymous
1. Create your own third degree polynomial that when divided by x + 2 has a remainder of –4. 2. Create your own division of polynomials problem. Demonstrate how this problem would be solved using both long division and synthetic division.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
what is the degree if you multiply x^2*(x+2) ?
anonymous
  • anonymous
\[\huge x^2(x+2) = \]
anonymous
  • anonymous
just multiply it out...

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anonymous
  • anonymous
not quite... \[\large x^2(x+2)=x^3+2x \]... agreed?
anonymous
  • anonymous
yes
anonymous
  • anonymous
so that's a third degree polynomial.. and what is the remainder if we take \(\large x^3+2x \) divided by \(\large x+2 \) ???
anonymous
  • anonymous
remember we just multiplied it out to get that third degree polynomial...
anonymous
  • anonymous
-4
anonymous
  • anonymous
no...
anonymous
  • anonymous
confused...................
anonymous
  • anonymous
if I ask you to multipl 2 times 3, what's the product?
anonymous
  • anonymous
**multiply...
anonymous
  • anonymous
6
anonymous
  • anonymous
now... what's the remainder if I ask you 6 divided by 3 ?
anonymous
  • anonymous
0
anonymous
  • anonymous
that's what i was asking in when we were working with the polynomial x^3 + 2x... the remainder when \(\large x^3+2x \) divided by \(\large x+2 \) is zero....
anonymous
  • anonymous
still with me?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
good... but we want a remainder of -4.... so what do you think we need to do?
anonymous
  • anonymous
not sure
anonymous
  • anonymous
|dw:1340429487175:dw|
anonymous
  • anonymous
we need to stick something in that box so that our remainder is -4....
anonymous
  • anonymous
take a wild guess...
anonymous
  • anonymous
ok... how 'bout this....
anonymous
  • anonymous
???
anonymous
  • anonymous
still there sara?
anonymous
  • anonymous
yeah what goes in the box?
anonymous
  • anonymous
ok... sorry.. i made some typos up there... but this should be more clear...
anonymous
  • anonymous
|dw:1340430131260:dw|
anonymous
  • anonymous
|dw:1340430256983:dw|
anonymous
  • anonymous
see the question mark? what should it be in order for our remainder to be -4?
anonymous
  • anonymous
-4
anonymous
  • anonymous
yes... i'm sorry i shuda done this way first.....
anonymous
  • anonymous
|dw:1340430491392:dw|
anonymous
  • anonymous
okay gottcha thats the equation thats is a third degree polynomial that when divided by x + 2 has a remainder of –4. :)
anonymous
  • anonymous
yes...:) again.... sorry....
anonymous
  • anonymous
its okay
anonymous
  • anonymous
thanks for sticking with me....:)

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