Simplify

[James Smithson]

Ok so I have been doing algebra for a few weeks at school but I am off school self iscolating and I dont know how to do the following. any help would be appreciated thanks in advance!!
simplify :
5x^2+15x-25
5x

I think I divide all by 5 but I have no idea why other than it looks good and seems to work ? as 5 15 and 25 all have 5 as a factor ???

 

[Dr.Peterson]

Ok so I have been doing algebra for a few weeks at school but I am off school self iscolating and I dont know how to do the following. any help would be appreciated thanks in advance!!
simplify :
5x^2+15x-25
5x

I think I divide all by 5 but I have no idea why other than it looks good and seems to work ? as 5 15 and 25 all have 5 as a factor ???

This depends somewhat on context, and certainly on the details of wording if you didn't quote everything.

If the topic is rational functions, then just dividing numerator and denominator by 5 would be appropriate, as the result would be a fraction.

If the topic is polynomials, then you would want to divide each term in the numerator by all of 5x, resulting in a polynomial plus a fraction.

This is the algebraic equivalent of whether 21/12 "simplifies" to 7/4 or to 1 3/4. It depends on what you want!

 

[James Smithson]

all it says is suimplify the following expressions as far as possible; multiply out brackets expand any formulars collect like terms and show working . Its only GCSE so Im guessing I dont understand what you said as its to advanced for me haha. thank you tho

This depends somewhat on context, and certainly on the details of wording if you didn't quote everything.

If the topic is rational functions, then just dividing numerator and denominator by 5 would be appropriate, as the result would be a fraction.

If the topic is polynomials, then you would want to divide each term in the numerator by all of 5x, resulting in a polynomial plus a fraction.

This is the algebraic equivalent of whether 21/12 "simplifies" to 7/4 or to 1 3/4. It depends on what you want!

 

[Dr.Peterson]

all it says is suimplify the following expressions as far as possible; multiply out brackets expand any formulars collect like terms and show working . Its only GCSE so Im guessing I dont understand what you said as its to advanced for me haha. thank you tho

No, nothing I said should be beyond what you are learning.

I was asking you to tell me what topic the problem was under. What are you studying specifically? If from a book or equivalent, what is the name of the chapter?

And if there is no specific context, then either of the answers I suggested should be valid.

I often say that "simplification is in the eye of the beholder". Both [MATH]\frac{x^2+3x-5}{x}[/MATH] and [MATH]x+3-\frac{5}{x}[/MATH] can be considered simple, for different purposes.

 

[Sarah.N]

I don't know what it exactly means by simplifying as far as possible,
but i simplify it like this:




i don't know if it helps or not.

I hope it was useful ;D

 

[Dr.Peterson]

I don't know what it exactly means by simplifying as far as possible,
but i simplify it like this:

i don't know if it helps or not.

I hope it was useful ;D

I don't see what your middle steps have to do with the work at all. They certainly don't make it any easier.

To obtain the answer you got (after fixing a typo), all you have to do is to divide each term by 5x:

[MATH]\frac{5x^2+15x-25}{5x} = \frac{5x^2}{5x} + \frac{15x}{5x} - \frac{25}{5x} =x+3-\frac{5}{x}[/MATH]​

 

[Sarah.N]

I don't see what your middle steps have to do with the work at all. They certainly don't make it any easier.

To obtain the answer you got (after fixing a typo), all you have to do is to divide each term by 5x:

[MATH]\frac{5x^2+15x-25}{5x} = \frac{5x^2}{5x} + \frac{15x}{5x} - \frac{25}{5x} =x+3-\frac{5}{x}[/MATH]​

yep, you're right
i just made it complicated