12ax^3+20bx^2+32cx
what does this equal when factored out??

- anonymous

12ax^3+20bx^2+32cx
what does this equal when factored out??

- chestercat

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- anonymous

What factors do all 3 terms have in common?

- 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

Ok, do you know what I mean by terms?

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## More answers

- anonymous

How many terms does the expression you gave have?

- anonymous

3

- anonymous

Right. Ok so lets look at the first term
\[12ax^3\]
That's saying \(12 \times a \times x^3\) right?

- anonymous

yeah

- 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

i dotn even know what factors are so yeah

- 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

So what are the different things you can multiply to get 12?

- anonymous

4 and 3 and 1 and 12

- anonymous

4*3, 1*12, and 6*2 right?

- anonymous

yeah

- 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

So lets look at the other 2 sets of factors.
4 and 3.

- anonymous

Err 4*3 and 6*2

- anonymous

Starting with 4*3. Now can either of those factors be factored further?

- anonymous

Remember to ignore factorizations that use a 1.

- anonymous

the 4

- anonymous

And its factors are?

- anonymous

2*2

- anonymous

Right. So putting it all together we have that 12 = 2*2*3

- anonymous

And if we factor the other way
12 = 6*2
= (3*2)*2
We get the same thing 2*2*3

- anonymous

So no matter how you factor something you will end up with the same factors.

- anonymous

So we can say that 12 has two factors of 2. And one factor of 3.

- anonymous

ok

- anonymous

Now then, what are the factors of \(x^2\)

- anonymous

Remember that \(x^2\) = x*x

- anonymous

x isnt a number so it doesnt have factors

- 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

right? Because \(x*x = x^2\)

- anonymous

yeah

- anonymous

Ok and a cannot be factored further cause we don't know what number it is either.

- 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

ok

- anonymous

Whoops, it should be \(12ax^3\). So that's 3 factors of x

- anonymous

So now you try to do the second term.

- anonymous

2*10 2*5

- anonymous

2*10 2*5

- anonymous

20 = 2*10
= 2*(2*5)
Is that what you mean?

- anonymous

it is now

- anonymous

Ok, so what are the factors of \(20bx^2\)

- anonymous

list them just like I did for \(12ax^3\)

- anonymous

2*5 b x*x

- anonymous

You're missing an extra factor of 2.

- anonymous

5*2 = 10, not 20

- anonymous

5*2*2 = 20

- anonymous

Try it again with the 3rd term just to be sure you have it down.

- anonymous

i dont know anything for 32 other than 32 and 1

- anonymous

Well it's an even number right?

- anonymous

So you know at least that it has a factor of 2.

- anonymous

yeah

- anonymous

So what times 2 is 32?

- anonymous

And if you aren't sure, how can you find out?

- anonymous

If 2*h = 32 then h = 32/2 right?

- anonymous

sorry my computetr is being extremely tarded and its pissing me off but its 16

- anonymous

sorry my computetr is being extremely tarded and its pissing me off but its 16

- anonymous

Ok right. And what are the factors of 16?

- anonymous

2*8

- anonymous

And the factors of 8?

- anonymous

2*4

- anonymous

And 4 can be factored

- anonymous

2*2

- anonymous

Ok let me show you a trick for keeping track of all this stuff.

- anonymous

http://www.dabbleboard.com/draw?b=Guest666631&i=0&c=3653c1e6f8130c42c19163377ccd7be35dcb8560

- anonymous

my computer keeps fluttering up and its pissing me off so i g2g

- anonymous

ok

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