Question

Need help with Algebra

I have to divide (16x^5y^4 + 6x^3y - 2x^2y - 24x^2y^4) by -2x^2y and I keep getting different answers.

Answer 1

Just to make sure the problem is copied correctly -- this is the fraction you have to reduce?
\[
\huge
\frac{16x^5y^4 + 6x^3y - 2x^2y - 24x^2y^4}{-2x^2y}
\]

Answer 2

yes

Answer 3

Good good.
Ok, start with the numerator (top). Look at the coefficients (16, 6, -2, -24) Do they have a common factor you can pull out?

Answer 4

for 16 is 4 a common factor?

Answer 5

4 is a factor of 16. But we want a factor that is common to all of the coefficients. So 4 won't work, because -2 is one of the coefficients.

Answer 6

oh okay i get it. so would it be 2?

Answer 7

No worries. Yes, 2 is the common factor. So you can now write
\[
\huge
\frac{2(8x^5y^4 + 3x^3y - 1x^2y - 12x^2y^4)}{-2x^2y}
\]
Note that already we can cancel the 2 in the numerator and the 2 in the denomiator:
\[
\huge
\frac{(8x^5y^4 + 3x^3y - 1x^2y - 12x^2y^4)}{-x^2y}
\]
Next - look at the \(x\) terms in the numerator. Can you factor out a power of \(
x\)?

Answer 8

could we factor out 5? since 5 isn't common to any of the coefficients.

Answer 9

Well not quite. We're looking to factor out the highest possible "x to a power".

A simpler case would be this:
\[
\huge x^5 + x^3 = x^3(x^2+1)
\]
Or
\[
\huge
x^{10}-x^5 +x^4 = x^4(x^6-x^1+1)
\]

So when you're looking at the numerator, look only at the "x to the power" and see if you can do the same thing. Ignore the other stuff (coefficients and powers of y) for now.

Answer 10

i think i'll be okay figuring it out now thank you for the help :)

Answer 11

Ok, good luck!

Answer 12

thank you :)