Question

Multiplying and Dividing Polynomials!!! Please help ASAP fan and medal!

Answer 1

X = r+2
Y = 2r+9
Z = r^2+17r+30

[XY - Z] / X

First, we need to find XY.
XY = X * Y = (r+2)(2r+9)
These can be FOILed together. Try it.

Answer 2

\[2r^2+13r+11\]

Answer 3

That's right, except for the last part. Remember, it's 2*9, not 2+9.

Answer 4

oh haha yeah 18

Answer 5

Yes! Now we need [XY - Z].
We know that XY = 2r^2 +13r +18, and Z = r^2 +17r +30.

XY - Z
(2r^2 +13r +18) - (r^2 +17r +30)
We need to distribute that - sign.
(2r^2 +13r +18) + (-r^2 -17r -30)
Now you can combine like terms.

Answer 6

2-4r-12 ??

Answer 7

r-24

Answer 8

Hey, thanks for that you two, but we're working it out by hand.
2r^2 - r^2 = r^2
13r - 17r = -4r
18 - 30 = -12

[XY - Z] = r^2 -4r -12.

Answer 9

haha oh duh I guess I'm brain dead today lol

Answer 10

No, it's okay. You got the second and third terms right. Now we have to divide by X, or r+2.

Answer 11

Are you familiar with polynomial long division or synthetic division?

Answer 12

I know of synthetic division, but I am don't understand either very well at all.... :\ I've only seen this..
http://www.wikihow.com/Divide-Polynomials-Using-Synthetic-Division

Answer 13

Sorry, lost connection there.

Synthetic division works for any polynomial divided by a binomial (two terms, something like (x-1)).

It works like this:
Top left box: second term in the binomial multiplied by -1.
ROW 1: Coefficients of each term in descending power order.
ROW 2: Blank for now.
line -----------
ROW 3: Drop the first number down, and leave the rest blank.

I'll outline a setup for you and walk you through solving it.