SOLUTION: When asked to factor completely a certain polynomial, four students gave the following answers: 3(x^2-2x-15); (3x-5)(5x-15); 3(x-5)(x-3) and (3x-15)(x-3).Which one is the correct a

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: When asked to factor completely a certain polynomial, four students gave the following answers: 3(x^2-2x-15); (3x-5)(5x-15); 3(x-5)(x-3) and (3x-15)(x-3).Which one is the correct a      Log On


   

Question 247194: When asked to factor completely a certain polynomial, four students gave the following answers: 3(x^2-2x-15); (3x-5)(5x-15); 3(x-5)(x-3) and (3x-15)(x-3).Which one is the correct answer? Why?
Found 2 solutions by Alan3354, College Student:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
When asked to factor completely a certain polynomial, four students gave the following answers: 3(x^2-2x-15); (3x-5)(5x-15); 3(x-5)(x-3) and (3x-15)(x-3).Which one is the correct answer? Why?
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Only this one is factored completely. That doesn't necessarily make it correct, but the others are eliminated.
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3(x-5)(x-3)

Answer by College Student(505) About Me  (Show Source):
You can put this solution on YOUR website!
3(x^2-2x-15)
We can factor this expression even further.
It would look like this: 3(x-5)(x+3), thus the given result was incomplete.

(3x-5)(5x-15)
We can factor (5x-15) even further into 5(x-3), thus this expression was also incomplete.

3(x-5)(x-3)
We can not factor this expression further, thus it is the correct answer to our problem.

(3x-15)(x-3)
We can factor 3 out of the first term, so it would look like this: 3(x-5)(x-3).
Therefore, this expression was also incomplete.

Here some more tips and examples on factoring.
http://www.mathsisfun.com/algebra/factoring.html