Problem with a factoring

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Marco_San

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May 31, 2022
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Hi, I have a problem with a factoring:
I need to factor: [imath]x^2 + 1.5 x - 10[/imath]
I tried and the result I can get is: [imath](x-2.5)(x+4)[/imath]
but apparently it's possible to factor even more, the result they ask me is: [imath](2x-5)(0.5x+2)[/imath]
I tried to use various calculators but the only one who can factor this it's Wolfram, which gives 2 results: what I got, and what I should get; but when I go to see the steps it just gives me those for the result that I got
That's why I'm here now, on this forum that I have just discovered but that I already like a lot, and I ask you for help :rolleyes:

Thanks for your time ?
 
Well, it's as I thought, I couldn't factoring it further .. but they told me it was possible
Thanks a lot for the reply ?

Oh, if you can, do you know any sites where I can practice factoring, and other algebra topics?
 
[math]x^2 + 1.5x - 10 = \dfrac{1}{2} * 2 * (x^2 + 1.5x - 20) = \dfrac{1}{2} * ( 2x^2 + 3x - 20) =\\ 0.5 * (2x - 5)(x + 4).[/math]
Depending on which factor you multiply by 0.5, you get two equally valid but superficially different results.
 
Marco_San said:
Hi, I have a problem with a factoring:
I need to factor: [imath]x^2 + 1.5 x - 10[/imath]
I tried and the result I can get is: [imath](x-2.5)(x+4)[/imath]
but apparently it's possible to factor even more, the result they ask me is: [imath](2x-5)(0.5x+2)[/imath]
I tried to use various calculators but the only one who can factor this it's Wolfram, which gives 2 results: what I got, and what I should get; but when I go to see the steps it just gives me those for the result that I got
That's why I'm here now, on this forum that I have just discovered but that I already like a lot, and I ask you for help :rolleyes:

Thanks for your time ?
Click to expand...
We commonly talk about "factoring over the integers", meaning that the coefficients must all be integers; that applies only when the original polynomial has integer coefficients. Lacking that, there are no restrictions, and all the answers that have been given are equally valid. I myself would have done something like what JeffM did, factoring out 1/2 to leave integer coefficients, and factoring that part over the integers. But that's largely a matter of habit.

It's also worth pointing out that when a textbook (or teacher) gives an answer, that doesn't mean that any other form would be considered wrong. You are generally expected to be able to see when your answer is equivalent, and therefore also acceptable. What they show is not the answer they demand of you, but the answer they got! There is no "should" about it.
 
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