anonymous
  • anonymous
12ax^3+20bx^2+32cx what does this equal when factored out??
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
What factors do all 3 terms have in common?
anonymous
  • anonymous
i dotn know none of tis makes any sense because my teacher doesnt teach any of the material he just throws the assighnmkent and tests in your face and expect you to know what to do
anonymous
  • anonymous
Ok, do you know what I mean by terms?

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anonymous
  • anonymous
How many terms does the expression you gave have?
anonymous
  • anonymous
3
anonymous
  • anonymous
Right. Ok so lets look at the first term \[12ax^3\] That's saying \(12 \times a \times x^3\) right?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
Ok, so 12, a, and \(x^3\) are factors of \(12ax^3\). But some of those can be factored further. 12 for example can be factored into what?
anonymous
  • anonymous
i dotn even know what factors are so yeah
anonymous
  • anonymous
Ok. Factors are like terms, but terms are for addition and subtraction. Factors are for multiplication and division. When I say \(3 \times 4\) = 12, I'm saying that 12 is the PRODUCT of the FACTORS 4 and 3.
anonymous
  • anonymous
So what are the different things you can multiply to get 12?
anonymous
  • anonymous
4 and 3 and 1 and 12
anonymous
  • anonymous
4*3, 1*12, and 6*2 right?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
We will ignore the factorization using 1's because you can have infinitely many 1's when you factor something, it's not very useful. 12*1 = 12, but 12*1*1*1*1*1 = 12 also.
anonymous
  • anonymous
So lets look at the other 2 sets of factors. 4 and 3.
anonymous
  • anonymous
Err 4*3 and 6*2
anonymous
  • anonymous
Starting with 4*3. Now can either of those factors be factored further?
anonymous
  • anonymous
Remember to ignore factorizations that use a 1.
anonymous
  • anonymous
the 4
anonymous
  • anonymous
And its factors are?
anonymous
  • anonymous
2*2
anonymous
  • anonymous
Right. So putting it all together we have that 12 = 2*2*3
anonymous
  • anonymous
And if we factor the other way 12 = 6*2 = (3*2)*2 We get the same thing 2*2*3
anonymous
  • anonymous
So no matter how you factor something you will end up with the same factors.
anonymous
  • anonymous
So we can say that 12 has two factors of 2. And one factor of 3.
anonymous
  • anonymous
ok
anonymous
  • anonymous
Now then, what are the factors of \(x^2\)
anonymous
  • anonymous
Remember that \(x^2\) = x*x
anonymous
  • anonymous
x isnt a number so it doesnt have factors
anonymous
  • anonymous
It is a number. We just don't know what number it is. So we can't factor further than x, but we do know that \(x^2\) has two factors of x.
anonymous
  • anonymous
right? Because \(x*x = x^2\)
anonymous
  • anonymous
yeah
anonymous
  • anonymous
Ok and a cannot be factored further cause we don't know what number it is either.
anonymous
  • anonymous
Ok, so now putting it all together we have that \(12ax^2\) has two factors of 2, one factor of 3, one factor of a, and two factors of x.
anonymous
  • anonymous
ok
anonymous
  • anonymous
Whoops, it should be \(12ax^3\). So that's 3 factors of x
anonymous
  • anonymous
So now you try to do the second term.
anonymous
  • anonymous
2*10 2*5
anonymous
  • anonymous
2*10 2*5
anonymous
  • anonymous
20 = 2*10 = 2*(2*5) Is that what you mean?
anonymous
  • anonymous
it is now
anonymous
  • anonymous
Ok, so what are the factors of \(20bx^2\)
anonymous
  • anonymous
list them just like I did for \(12ax^3\)
anonymous
  • anonymous
2*5 b x*x
anonymous
  • anonymous
You're missing an extra factor of 2.
anonymous
  • anonymous
5*2 = 10, not 20
anonymous
  • anonymous
5*2*2 = 20
anonymous
  • anonymous
Try it again with the 3rd term just to be sure you have it down.
anonymous
  • anonymous
i dont know anything for 32 other than 32 and 1
anonymous
  • anonymous
Well it's an even number right?
anonymous
  • anonymous
So you know at least that it has a factor of 2.
anonymous
  • anonymous
yeah
anonymous
  • anonymous
So what times 2 is 32?
anonymous
  • anonymous
And if you aren't sure, how can you find out?
anonymous
  • anonymous
If 2*h = 32 then h = 32/2 right?
anonymous
  • anonymous
sorry my computetr is being extremely tarded and its pissing me off but its 16
anonymous
  • anonymous
sorry my computetr is being extremely tarded and its pissing me off but its 16
anonymous
  • anonymous
Ok right. And what are the factors of 16?
anonymous
  • anonymous
2*8
anonymous
  • anonymous
And the factors of 8?
anonymous
  • anonymous
2*4
anonymous
  • anonymous
And 4 can be factored
anonymous
  • anonymous
2*2
anonymous
  • anonymous
Ok let me show you a trick for keeping track of all this stuff.
anonymous
  • anonymous
http://www.dabbleboard.com/draw?b=Guest666631&i=0&c=3653c1e6f8130c42c19163377ccd7be35dcb8560
anonymous
  • anonymous
my computer keeps fluttering up and its pissing me off so i g2g
anonymous
  • anonymous
ok

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