Can someone help me divide this? I cannot use long division. (a^3x^4-a^2x^3)/(-ax^2). Can someone go though the steps with me?

Question

calculusfunctions · Answer

$$\frac{ a ^{3}x ^{4}-a ^{2}x ^{3} }{ -ax ^{2} }$$Is this the correct expression?

anonymous · Answer

Yessir.

calculusfunctions · Answer

Alrighty then first do you notice that you can factor the numerator?

anonymous · Answer

WHat do you mean factor it?

calculusfunctions · Answer

You haven't learned factoring polynomials?

anonymous · Answer

Yes, but I was absent that day...stupid I know..

calculusfunctions · Answer

No, not stupid at all if you had a valid reason. OK so the first rule of factoring polynomials is to always look for the greatest common factor. What do you think that would be in this case for the numerator?

calculusfunctions · Answer

After this I will also teach you an alternate method. Don't worry, it's not long division.

anonymous · Answer

x^2?...

calculusfunctions · Answer

Actually a²x³. Can you see why?

anonymous · Answer

No.

calculusfunctions · Answer

You have (a³xˆ4 - a²x³) in the numerator. a  and  x appear in both terms. The least exponent of a is 2 and the least exponent of x is 3. Therefore the greatest common factor is  a²x³.  That is how you find the greatest common factor, understand?

anonymous · Answer

Yes.

calculusfunctions · Answer

Now we would have  a²x³(ax - 1) in the numerator. Understand?

calculusfunctions · Answer

We now have$$\frac{ a ^{2}x ^{2}(ax -1) }{ -ax ^{2} }$$Right?

anonymous · Answer

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