Solve by factoring

[Timbro]

Okay so I have an assignment question that is solve by factoring.

2x^2-11x+15-(x+3)(2x-5)=0

So if I multiply out the factored terms, add like terms, solve for x etc I get x=5/2

I'm not sure if thats what the question is asking though.

So I can factor to (2x-5)(x-3)-(x+3)(2-5)=0 but I dont know where to go from there do I have to plug in x=3,-3,5/2 just to prove the answer is actually x=5/2 or just leave it in that factored form. Or is there some special factoring form I'm missing. Is it difference of two squares or square of a difference. Just not sure where to go. Any help appreciated

 

[mmm4444bot]

solve by factoring.

2x^2-11x+15-(x+3)(2x-5)=0

if I multiply out the factored terms, add like terms, solve for x etc I get x=5/2 That's the correct answer.

I'm not sure if thats what the question is asking though.

So I can factor to (2x-5)(x-3)-(x+3)(2x-5)=0 but I dont know where to go from there

To show solution by factoring, note that you have the same factor 2x-5 on each side of the red subtraction above.

Factor 2x-5 out of that subtraction.

(2x-5)*[(x-3) - (x+3)] = 0

Simplify, and continue.

 

[Timbro]

Simplify, and continue.[/QUOTE]

Thanks for your help but that is the sort of maths language I struggle with. How do I simplify and continue?

The word simplify causes me untold grief. It is so poorly defined. I asked my tutor what it means when a question in a textbook asks to simplify and even he says its vague.

I don't know how to continue to simplify from this point if it's in factors and it is asked to be solved by factoring. Sorry it's been a long week of trying to wrap my head around a lot of topics. Mature age student going back to maths after 13 years out of high school so I'm very confused and tired. It gets frustrating spending hours on simple questions. I would really appreciate if you could elaborate some.

Cheers Tim

 

[mmm4444bot]

How do I simplify and continue?

The word simplify causes me untold grief. It is so poorly defined.

Hi Tim, in this context, the instruction to simplify means to combine "like terms". It's basically arithmetic with signed numbers (i.e., positives and negatives), and some things called "The Order of Operations" and "The Commutative Property of Addition".

To simplify the expression (x-3) - (x+3), we recognize that this is just addition and subtraction (i.e., no multiplication or division operations), and so we realize from the order of operations that the first set of parentheses are unnecessary.

x - 3 - (x + 3)

The order of operations also explains how the remaining set of parentheses indicate that both numbers shown in red above are being subtracted. In other words, if we rewrite as subtract x and subtract 3, we may remove the remaining parentheses.

x - 3 - x - 3

Next, with understanding that subtraction may be thought of as an abbreviation for "adding the opposite", we can view all of the subtractions above as additions, instead.

x + (-3) + (-x) + (-3)

The commutative property of addition says that -- when adding a bunch of numbers -- you may add them in any order.

x + (-x) + (-3) + (-3)

Now, it's simply a matter of arithmetic. We call this last step "combining like-terms". The positive x and the negative x are both like each other (they are both variables); the two (-3) being added are also like each other (they are both constants).

Adding positive x and negative x together gives zero, because they are opposites.

Adding negative 3 to negative 3 gives negative 6.

0 + (-6) = -6

In other words, the factorization

(2x-5)*[(x-3) - (x+3)]

simplifies to

(2x-5)*(-6)

Each of the topics that I mentioned above comes from introductory algebra (aka: pre-algebra).

Understanding things like order of operations, commutativity of certain operations, correct perception of negative signs in their various contexts, and combining like-terms make up a "tool kit" of knowledge for handling new material. In other words, learning math is progressive.

If you've forgotten a lot of prerequisites, you may need a crash review.

The instruction "to simplify" does become more involved, as one progresses through new material (eg: simplifying radicals), but this does not happen in a vague manner. You just need the basic tool kit, to understand how to proceed.

Right now, it seems like your tool kit is kinda empty, for the level of exercise posted. What class are you currently taking? Is this an on-line course? Were you required to take a placement exam? (I'm always curious to know how students get into this type of situation because schools have a responsibility to ensure that students are ready for their classes.)

Cheers ~ Mark

PS: I'm thinking that you ought to consider looking for a different tutor. The simplification above is not at all a vague process. It just takes practice, starting at the beginning and moving forward. If you practice enough, you will reach a point where you go from (x-3)-(x+3) to -6 in your head. You will skip some steps; for instance, you will see +x somewhere in an expression, and you will see -x somewhere else in the expression. You will simply cancel them; you won't actually use commutativity to rearrange them next to one another. You will see two opposites that cancel. That algebra tutor should have been able to explain all of this to you. Seriously, Tim, look for a more-qualified tutor. :cool: