Question

Factor the following expression completely:
-6x^3 – 20x^2 + 16x

Answer 1

GCF?

Answer 2

4

Answer 3

Did you tried anything ?

Answer 4

not quite, look at the x's
plus, what is -6/4 ?
not an integer.

Answer 5

Let's also factor out the negative sign and an _?

Answer 6

\( -6 x^3 - 20 x^2 + 16 x =-2 x (4+x) (-2+3 x) \)

Answer 7

The GFC is 2

Answer 8

Hey fool I was trying to figure it out

Answer 9

u forgot the x sinz

Answer 10

-2x
is the GFC
try to confirm FFM's answer... maybe he's wrong.

Answer 11

lol, yeah I could be wrong.

Answer 12

human errors do occur..

Answer 13

Yeah, provided I am human though ...

Answer 14

http://www.wolframalpha.com/input/?i=-6x%5E3+%E2%80%93+20x%5E2+%2B+16x

Answer 15

-2x(4+x)(-2+3x) = -6x^3 - 20x^2 + 16x

Answer 16

yeah he was right?

Answer 17

well that's one way to confirm FFM's answer
I was hoping you'd try to pull out a -2x though, for practice on factoring.

Answer 18

yeah I am but when you have 6 different people telling you how to do it it is hard

Answer 19

-6x^3 - 20x^2 + 16x =-2x(3x^2)-2x(10x)-2x(-8)=-2x(3x^2+10x-8)
ca you finish?

Answer 20

can*

Answer 21

-6x^3 - 20x^2 + 16x =-2x(3x^2)-2x(10x)-2x(-8)=-2x(3x^2+10x-8)=
-6x^3 - 20x^2 + 16x right?

Answer 22

-2*3 is -6 -2*10= 20 -2*-8 = 16 then you add the different powers together

Answer 23

I meant the exponents

Answer 24

Yes but not quite what I asked you to do...
I want to see if you can get FFM's answer on your own.
so we have
-2x(3x^2+10x-8)
can you factor the
(3x^2+10x-8) part? that will either confirm or deny the answer FFM gave once and for all.

Answer 25

typo...
what is
3x^2+10x-8
factored?

Answer 26

okay lets see
(2x+x)(5-4) right?

Answer 27

or is it backwards

Answer 28

should it be (2x+5)(x-4)

Answer 29

no...
\[(2x+x)(5-4)=3x(1)=3x\neq3x^2+10x-8\]you need one x term iun each set of parentheses
ccloser, but you wont get the 3x term from above\[(2x+5)(x-4)=2x^2+x-20\]so keep trying.

Answer 30

one thing you know is that because x^2 has a 3 next to it, the factorization will be\[(3x\pm?)(x\pm?)\]because that is the only way to get the three to show up...

Answer 31

okay (3x + 4)(x + 2) does this look right?

Answer 32

multiply it out and see

Answer 33

\[(3x+4)(x+2)=3x^2+2x+4x+8=3x^2+6x+8\]
in order to get the -20 to show we need at least to have\[(3x\pm4)(x\pm5)\]or the other way\[(3x\pm5)(x\pm4)\]that way we make sure we have the 3 at the beginning and the -20 at the end...

Answer 34

okay but to factor 3x^2 + 10x - 8 it Factors to:
(3x - 2)(x + 4) = 0

Answer 35

A good strategy is to look at the first and last terms.
That tell you a lot about how it can be factored.

Let's try yours\[(3x-2)(x+4)=3x^2-2x+12x-8=3x^2+10x-8\]so it looks like that works!
(disregard what I said about the -20, I forgot what we were trying to factor :/ )
now does that give the same answer as FFM ?

Answer 36

yes it does

Answer 37

Well I guess it was all for nothing then, might as well just take his word blindly from now on...
Yeah right!!!

Answer 38

I think so he has it backwards though

Answer 39

right, but it is ok
he took the negative of each term in the parentheses
and
(-1)(-1)=1
so they are the same

Answer 40

he has it to where it is (4+x)(-2+3x) so no it doesn't add up to the -20

Answer 41

for the x it will
Like I said I got confused and forgot what we were trying to factor
what I meant is that the produce of the two constants should be -8 like in the original, which he has.

Answer 42

okay so he was right then?

Answer 43

product* lol
yes he was right
multiply both you and his answer out and you get the same

Answer 44

your*
cannot type today

Answer 45

okay so do you think I did okay on the factoring part then?

Answer 46

I thin you need practice.
If you want that get a deck of 3x5 cards and write out various products like

(x+2)(x+4)=x^2+6x+8
(2x-5)(x+7)=2x^2+2x-35
(3x-1)(2x+2)=6x^2+4x-2

(just write the right-hand side, the result of the multiplication)
and write them out onto the card. Then shuffle them and see if you can run the process backwards:

x^2+6x+8=???
2x^2+2x+35=???
6x^2+4x-2=???

when you can do that then you have factoring down!

Answer 47

think*

Answer 48

Alright that sounds like it should be fun

Answer 49

right?
enjoy :D

Answer 50

you too and thank you again