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.

 

[CellCoree]

There are a few strategies that you can use to check your algebraic long division before submitting your answer. One approach is to double check your multiplication steps by using the distributive property. For example, if you are supposed to multiply 2a by 2, you can rewrite it as 2 x (2a) and then use the distributive property to get 4a. This can help you catch any errors in your multiplication.

Another strategy is to plug your final answer back into the original equation and see if it works. For example, if you are dividing 6a^2 + 4a by 2a, your final answer should be 3a + 2. You can then plug this answer back into the original equation and see if it works out correctly.

Additionally, you can also use a calculator to check your work. Most calculators have a built-in function for algebraic long division, so you can compare your answer to the calculator's answer to see if they match.

Lastly, it's always a good idea to review the steps of algebraic long division and make sure you are following them correctly. Sometimes, simple mistakes can be avoided by double checking your work and following the correct steps.