Can someone please help me with my final exam review?

Isn’t that cheating?

Why would it be cheating? It’s a study guide to help me prepare for the final exam. I’ve done all the questions but there are a few questions that I don’t understand…so to answer your question…no it’s not cheating.

For 19, use Google to find a definition and example for extraneous solutions. #22 is made simpler when setting x = a^2.

How about the last one?

For #19:
Just guessing here… but it seems that one of the ‘extraneous solutions’ that can occur is something like: x^2 + 4 = 0. It’s an impossible solution, since a square of a number will never be negative. But I don’t really know how to answer the question about “these two types of equations”. Equations that have impossible roots are unresolvable.

For #22:
a^4 – 7a^2 + 12 = 0 resolves to:
(a^2 – 4) * (a^2 – 3) = 0

So the two solutions are a = 2 or a = sqrt of 3

I can’t make sense of the second equation listed under that… it seems to be two equations mixed together somehow.

I’m guessing the (3x-12)(X=5)(2x-3)>0 Should be (3x-12)(X+5)(2x-3)>0 . Right?

@worriedguy. yeah you’re right..oops

For the last one, here is a hint.

If you multiple 3 numbers and you want the product to be positive, you need either
a) all should be positive
b) two should be negative and one positive

Also, none of the numbers should be zero.

Make a number line for x and see where that takes you…

For #22, you just factor the term. Your final solution will look something like:
(a^2 + or – n) * (a^2 + or – m)

You know it’s a^2 in front because it’s often just the square root of the first term. The tricky part is figuring out n and m. The way to think about it english is “what two numbers add up to -7 and multiply to 12?” When you multiply the two terms, you can see that’s the same mathematically at that sentence. Solving that problem can be tricky, and I’ve found the easiest way is to intuit it… there’s usually only a few ways it can go. (In your head, think of which factors of twelve could add to 7): 3 and 4! And clearly they’ll both have to be negative.

so your solution is

(a^2 – 4 ) * (a^2 + – 3)

And you can verify by multiplying it out.

Makes sense? Read more on wikipedia