Question

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

Answer 1

What factors do all 3 terms have in common?

Answer 2

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

Answer 3

Ok, do you know what I mean by terms?

Answer 4

How many terms does the expression you gave have?

Answer 5

3

Answer 6

Right. Ok so lets look at the first term

\[12ax^3\]

That's saying \(12 \times a \times x^3\) right?

Answer 7

yeah

Answer 8

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?

Answer 9

i dotn even know what factors are so yeah

Answer 10

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.

Answer 11

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

Answer 12

4 and 3 and 1 and 12

Answer 13

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

Answer 14

yeah

Answer 15

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.

Answer 16

So lets look at the other 2 sets of factors.

4 and 3.

Answer 17

Err 4*3 and 6*2

Answer 18

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

Answer 19

Remember to ignore factorizations that use a 1.

Answer 20

the 4

Answer 21

And its factors are?

Answer 22

2*2

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

ok

Answer 28

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

Answer 29

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

Answer 30

x isnt a number so it doesnt have factors

Answer 31

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.

Answer 32

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

Answer 33

yeah

Answer 34

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

Answer 35

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.

Answer 36

ok

Answer 37

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

Answer 38

So now you try to do the second term.

Answer 39

2*10 2*5

Answer 40

2*10 2*5

Answer 41

20 = 2*10
= 2*(2*5)

Is that what you mean?

Answer 42

it is now

Answer 43

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

Answer 44

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

Answer 45

2*5 b x*x

Answer 46

You're missing an extra factor of 2.

Answer 47

5*2 = 10, not 20

Answer 48

5*2*2 = 20

Answer 49

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

Answer 50

i dont know anything for 32 other than 32 and 1

Answer 51

Well it's an even number right?

Answer 52

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

Answer 53

yeah

Answer 54

So what times 2 is 32?

Answer 55

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

Answer 56

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

Answer 57

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

Answer 58

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

Answer 59

Ok right. And what are the factors of 16?

Answer 60

2*8

Answer 61

And the factors of 8?

Answer 62

2*4

Answer 63

And 4 can be factored

Answer 64

2*2

Answer 65

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

Answer 66

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

Answer 67

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

Answer 68

ok