Factoring

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Hey guys,I have a question regarding factoring.Is there more than 1 answer to factoring?As In the following

Factor 7n^2-28n
My answer=7(n^2-4n)
Textbook=7n(n-4)

Factor 50n^4-25n^3
my answer=5n^2(10n^2-5n)
text book=25n^3(2n-1)

Even though both gives the same answers,but the text book states that you have to find a common factor between the 2 which is 7N.So I'm unsure if this is correct even though my answer still gives the same answer.
 
Hey guys,I have a question regarding factoring.Is there more than 1 answer to factoring?As In the following

Factor 7n^2-28n
My answer=7(n^2-4n)
Textbook=7n(n-4)

Factor 50n^4-25n^3
my answer=5n^2(10n^2-5n)
text book=25n^3(2n-1)

Even though both gives the same answers,but the text book states that you have to find a common factor between the 2 which is 7N.So I'm unsure if this is correct even though my answer still gives the same answer.

Although the answers are equivalent, what is generally meant by factoring is complete factoring. That means to reduce everything to constants and linear terms as much as possible. So, for example, since (n^2-4n) can be factored into the two linear terms n and (n-4) the textbook answer of 7n(n-4) is what is expected.

However suppose the expression had been 7n2+28. We have
7n2+28 = 7(n2+4)
and that is as far as you can go at the Beginning Algebra level.
 
Although the answers are equivalent, what is generally meant by factoring is complete factoring. That means to reduce everything to constants and linear terms as much as possible. So, for example, since (n^2-4n) can be factored into the two linear terms n and (n-4) the textbook answer of 7n(n-4) is what is expected.

However suppose the expression had been 7n2+28. We have
7n2+28 = 7(n2+4)
and that is as far as you can go at the Beginning Algebra level.


Thank you sir,always a pleasure. That's what I figured, I felt like something was off but couldn't clearly pinpoint it even though both gave the same answers.
 
Always a pleasure sir and thank you again.Had a feeling something was off.
 
Factor 7n^2-28n
My answer=7(n^2-4n)
Textbook=7n(n-4)

Even though both gives the same answers,
but the text book states that you have to find a > > common factor < <
between the 2 [two], which is 7N.

The textbook should be stating you have to find the "greatest common factor,"
in order to arrive at a complete factorization, not just a "common factor."
 
The textbook should be stating you have to find the "greatest common factor,"
in order to arrive at a complete factorization, not just a "common factor."


Ya I look back and finally notice that.Before I didn't notice because within the text book,it said FACTORING USING THE GREATEST COMMON FACTOR as the title but then I sorta ignored the title and just read the instruction in which it stopped using the term greatest common factor and just used common factor:oops:Hahaha seriously,my head hurts sometimes:p
 
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