1. ## Basic Factoring question

Expression $\displaystyle 28xy^2-14x$
my solution = $\displaystyle 14x(2y^2-1)$ or could also be $\displaystyle -14x(-2y^2+1)$

The book lists the solution as $\displaystyle -7x(-4y^2+2)$, are they both correct? And how do I know what to factor out to get consistent numbers with the book? In general I always factor out the largest possible number, in this case 14.

2. Originally Posted by allyourbass2212
Expression $\displaystyle 28xy^2-14x$
my solution = $\displaystyle 14x(2y^2-1)$ or could also be $\displaystyle -14x(-2y^2+1)$

The book lists the solution as $\displaystyle -7x(-4y^2+2)$, are they both correct? And how do I know what to factor out to get consistent numbers with the book? In general I always factor out the largest possible number, in this case 14.
Yes, all those solutions are equal to each other. It is very unusual of your textbook to factor out -7x rather than 14x. Perhaps it's because -4y^2+2 is a better form to solve a subsequent question.

3. Originally Posted by allyourbass2212
Expression $\displaystyle 28xy^2-14x$
my solution = $\displaystyle 14x(2y^2-1)$ or could also be $\displaystyle -14x(-2y^2+1)$

The book lists the solution as $\displaystyle -7x(-4y^2+2)$, are they both correct? And how do I know what to factor out to get consistent numbers with the book? In general I always factor out the largest possible number, in this case 14.
the two are correct but I prefer your solution

4. Originally Posted by allyourbass2212
The book lists the solution as $\displaystyle -7x(-4y^2+2)$, are they both correct? And how do I know what to factor out to get consistent numbers with the book?
Finding the Greatest Common Factor(GCF), as you did, is great and will yield the most simplified version of the expression. As you pointed out the author did not completely factor out the expression and did not utilize the GCF(14) as you did.

So you may continue to factor it $\displaystyle -7x(-4y^2+2)$, factor out 2 and get $\displaystyle -7x(2(-2y^2+1)=-14x(-2y^2+1)$

Good job