Algebra question - when you mult. a term in an algebraic fract by negative 1 ?

[74Heaven]

In Videotext today my dtr had this problem about simplifying a polynomial. I don't understand if her answer is correct or not?

14-19x-3x^2 (so 3 times x squared)
_____________ (this line is the fraction bar)

3x^2 - 23x +14

the next part was
(-1) 3x^2+19x-14 then (-1)(3x-2)(x+7) (-1)(x+7)
_______________ _____________ (after cancelling)= _____________
3x^2 - 23x +14 (3x-2)(x-7) (x-7)

The answer key ended up with the fllg. final answer
-x - 7
_______
x-7



I have a few questions:

Would the opposite answer be correct as well? such as mult both sides by neg 1 at the end:
(x+7)
____
(-x+7)
What is the property (or practice) called when you mult. by neg. 1 to get the signs to match when num/denominator expressions are so similar? (I'd like to look it up in another alg. book or online to get a better understanding?)

Why can we take just one part of the problem (i.e. the denominator or divisor?) and mult by -1 and not follow the algebraic rule that says we have to do the same thing for "both sides" of the problem?

Thanks, we are on day 3 of this now (Mod D, Unit VI, Les 1)
Lisaj - ljdeerparkATaolDOTcom

[Laura Corin]

Why can we take just one part of the problem (i.e. the denominator or divisor?) and mult by -1 and not follow the algebraic rule that says we have to do the same thing for "both sides" of the problem?


You are not actually changing it. You are writing exactly the same value in a different way. You therefore don't have to do the same to the bottom value.

Best wishes

Laura

[Pamela H in Texas]

Lisa,

When you have questions like this, the best way to find out if what you are thinking will work is to plug in a number (I like to use 3 just in case) and see if it works.

For example, in the above question, if you plug in 3 for X, you get 5/2 for the book's answer and 5/2 for your daughter's answer. So it looks like it works. Try again with 0 and -2 and see what you get.

Does that make sense? Testing answers is a skill that really works well. Even on the SAT and such, your student may not know how to figure the answer but if she knows how to plug in the answers given, she'll be able to get a couple more problems correct :)

HTHs,

[Jann in TX]

The answer the text gave was in proper form.

It is NOT proper to have a negative variable leading in the denominator.

It is OK to have a negative variable in the numerator.

The results (their answer and yours) are equivalent--but theirs is 'proper'. So yes--if you multiply both the numerator and denominator by a negative 1 the 'value' of the answer is preserved.

Identity property of multiplication (multiplying a value by '1' does not change value). When you multiply a fraction by negative 1/negative 1 you are multiplying it by a 'value' of positive 1.