Factoring-Please Help!

[unreal]

Ok we just got into this stuff in Alg. II and I can't figure out for the life of me how to do these, we worked on them in groups at school so I had help on the other ones but these last ones are the ones I didn't get done, I have looked on the internet how to do them, my parents are oblivious to this stuff, etc.

So if anyone can help me with these I would really appreciate it.

Also if you know the answers could you show me how you did them in a step by step format as well as the answer, then I could write them down in my notebook to study later, I really want to understand this stuff, don't even remember how to start and those infosites are crap with more advanced probs, at least the ones i was at.

Factoring:

1. 3a2-24a+48

2. 3x2+xy-6x-2y


3. 52-5st-14t2


4. 6x2+13x-5

Setting to Zero

1.y3+5y2+4y=0


2. (d-3)(d+5)=-12

Also my teacher said there is a possibility that any of these may be prime.

Thnx a bunch.

 

[daon]

1. Always eliminate the coefficient of the squared term if there won't be any fractions as a result.
2. Look for two numbers that when added together equal the coefficient of the middle term and that multiply to be the last term.

Ex:

\(\displaystyle 3a^2-24a+48\)

Look at the coefficient of a². Does each term have the 3 in common? Yes, they are all divisible by three, so you can "take out" a 3, and divide every term by 3.

So,

\(\displaystyle 3a^2-24a+48=3(\frac{3a^2}{3}-\frac{24a}{3}+\frac{48}{3})=3(a^2-8a+16)\)

Now, the 3 is out of the way, so we have to factor \(\displaystyle a^2-8a+16\)

What 2 numbers add together to equal -8, but multiply to +16? Dont feel discouraged if you don't know it right away, some of these problems take patience and trial and error. The two numbers are -4 and -4. So you write a^2-8a+16 = (a+ -4)(a+ -4) = (a-4)²

Substituting in to what we had before: \(\displaystyle 3a^2-24a+48 = 3(a^2-8a+16) = 3(a-4)^2\)

 

[unreal]

thanks ill do that in a few! do all the other problems work the same way or?