# polynomial Qs: 6c^3 + 7c^2 - 38c + 24 / 3c - 4, etc.

#### Princezz3286

##### Junior Member
a: the directions are to divide

6c^3 + 7c^2 - 38c + 24 / 3c - 4
I tried to group it and reduce but I have a feeling that is not right......
How do I start this problem?

b: for this problem it says to multiply and simplify....
w^2 - 3w -54/w^3 - 8w^2 X w/(w + 6)

this one we can factor to be
(w -9)(w + 6)/w^2(w - 8) X w / (w + 6) then I cancelled the (w + 6)'s
but now what? do I have to distribute the other w left on top to get w^2 - 9w/ w^2 (w - 8) and then cancel the w^2's? then I'd be left with
-9w/w - 8

#### stapel

##### Super Moderator
Staff member
Princezz3286 said:
a: the directions are to divide: 6c^3 + 7c^2 - 38c + 24 / 3c - 4
As posted, the above means the following:

. . . . .$$\displaystyle 6c^3\, +\, 7c^2\, -\, 38c\, +\, \frac{24}{3x}\, -\, 4$$

Is this what you meant? Or did you mean the following?

. . . . .$$\displaystyle \frac{6c^3\, +\, 7c^2\, -\, 38c\, +\, 24}{3c\, -\, 4}$$

Or something else?

Have you learned how to do long polynomial division yet?

Princezz3286 said:
b: for this problem it says to multiply and simplify: w^2 - 3w -54/w^3 - 8w^2 X w/(w + 6)
I think you are using the variable "X" to indicate multiplication, and I think you omitted grouping symbols, so the above is meant actually to be as follows:

. . . . .$$\displaystyle \left(\frac{w^2\, -\, 3w\, -\, 54}{w^3\, -\, 8w^2}\right)\, \left(\frac{w}{w\, +\, 6}\right)$$

Your work done appears to have been as follows:

. . . . .$$\displaystyle \left(\frac{(w\, -\, 9)(w\, +\, 6)}{w^2(w\, -\, 8)}\right)\, \left(\frac{w}{w\, +\, 6}\right)$$

. . . . .$$\displaystyle \left(\frac{w\, -\, 9}{w^2(w\, -\, 8)}\right)\, \left(\frac{w}{1}\right)$$

. . . . .$$\displaystyle \left(\frac{w\, -\, 9}{w(w\, -\, 8)}\right)\, \left(\frac{1}{1}\right)$$

. . . . .$$\displaystyle \frac{w\, -\, 9}{w(w\, -\, 8)}$$

How are you getting "-9w" as a numerator?

Please reply showing those steps (or correcting my guesses above). Thank you!

Eliz.

#### Princezz3286

##### Junior Member
Oh, I too the w and re-distributed it into the w - 9 and cancelled the w^2 I see, I see.... and yes, your set up was correct

Thank You!