How to check algebraic long division?

[Tyrion101]

My errors all involve multiplying numbers that look the same, for instance if there is a 2 that I'm supposed to multiply by a 2a I'll put 2 a, and not think about it till I see I got the answer wrong. Is there a way I can do something to the answer to see if it is right before I submit it?

 

[economicsnerd]

Division is just multiplication backward. Multiplication is usually much easier and less error-prone. If I understand correctly, you're asking: "If I try to compute f/g and get answer h, how do I check whether it's correct?" If that's the question, then a quick check is to compute g*h and see whether you get f.

 

[symbolipoint]

My errors all involve multiplying numbers that look the same, for instance if there is a 2 that I'm supposed to multiply by a 2a I'll put 2 a, and not think about it till I see I got the answer wrong.

Multiplying the individual terms requires a little bit of conscious focus. One must watch what one is doing.

Is there a way I can do something to the answer to see if it is right before I submit it?

Yes. Multiply the resulting quotient by the divisor. When you simplify this multiplication, to general form, it must match the dividend.

 

[Tyrion101]

Don't know why it didn't occur to me, but that makes sense. Thanks.