Optimal Methods for Factoring Equations

[uperkurk]

I'm factoring some equations and the way I do it seems correct and Wolfram often lists my way of factoring it but it's like the 5th or 6th one down.

Just wondering if it's like fractions where the best answer is the lowest the fraction can be reduced to.

For example I say that:

$$3a+6a^2+15a^3 = 3a(1+2a+5a^2)$$

Wolfram doesn't list my way of factoring it when I input the equation to be factored, but I know it's correct because when I input my factored form instead of the original problem, it lists the original problem as a solution.

Any particular way to be factoring these? Like highest exponenets first, not using 1 ect?

 

[HallsofIvy]

I'm factoring some equations and the way I do it seems correct and Wolfram often lists my way of factoring it but it's like the 5th or 6th one down.

Just wondering if it's like fractions where the best answer is the lowest the fraction can be reduced to.

For example I say that:

$$3a+6a^2+15a^3 = 3a(1+2a+5a^2)$$

That is simply the "distributive law": a(b+ c)= ab+ ac.

Wolfram doesn't list my way of factoring it when I input the equation to be factored, but I know it's correct because when I input my factored form instead of the original problem, it lists the original problem as a solution.

I am puzzled by your saying this. When I put "3a+ 6a^3+ 15a^3" into Wolfram alpha, it gives me quite a lot of information- such as the real root, 0, and two complex roots, and one thing it tells me is that it can also be written as "3a(5a^2+ 2a+ 1)".

Any particular way to be factoring these? Like highest exponenets first, not using 1 ect?

 

[ramsey2879]

I'm factoring some equations and the way I do it seems correct and Wolfram often lists my way of factoring it but it's like the 5th or 6th one down.

Just wondering if it's like fractions where the best answer is the lowest the fraction can be reduced to.

For example I say that:

$$3a+6a^2+15a^3 = 3a(1+2a+5a^2)$$

Wolfram doesn't list my way of factoring it when I input the equation to be factored, but I know it's correct because when I input my factored form instead of the original problem, it lists the original problem as a solution.

Any particular way to be factoring these? Like highest exponenets first, not using 1 ect?

Mathematica 8 gives your answer with either of the following inputs: Factor[3 x + 6 x^2 + 15 x^3] or Factor[3x + 6x^2 + 15x^3]. What version or format are you using? Note "Factor" must begin with a capital F and the expression must be put within square brackets, etc.

 

[uperkurk]

What I mean is which is prefered?

http://www4c.wolframalpha.com/Calculate/MSP/MSP28661e08b41157f5gd7f000040c225hah823i3e2?MSPStoreType=image/gif&s=44&w=117.&h=18.

http://www4c.wolframalpha.com/Calculate/MSP/MSP6901egf7iaae09973c30000473gfi1489a2g5df?MSPStoreType=image/gif&s=62&w=120.&h=18.

http://www4c.wolframalpha.com/Calculate/MSP/MSP37931i702gba3e39i9350000348g19dci0927517?MSPStoreType=image/gif&s=16&w=116.&h=22.

Are these all completely 100% equivalent or would an examiner prefer to see a certain layout?

 

[ramsey2879]

What I mean is which is prefered?

http://www4c.wolframalpha.com/Calculate/MSP/MSP28661e08b41157f5gd7f000040c225hah823i3e2?MSPStoreType=image/gif&s=44&w=117.&h=18.

http://www4c.wolframalpha.com/Calculate/MSP/MSP6901egf7iaae09973c30000473gfi1489a2g5df?MSPStoreType=image/gif&s=62&w=120.&h=18.

http://www4c.wolframalpha.com/Calculate/MSP/MSP37931i702gba3e39i9350000348g19dci0927517?MSPStoreType=image/gif&s=16&w=116.&h=22.

Are these all completely 100% equivalent or would an examiner prefer to see a certain layout?

I don't know what an examiner would prefer, but the layout you used in the original post is both my preferred way and what Mathematical used. I don't see a bunch of choices like you suggested. Mathematica 8 only gave me 3 a ( 1 + 2 a + 5 a^2)!