Question

please help i dont understand! factor completely. If a polynomial is prime, state this. -12x^2-28x+24

Answer 1

All the coefficients are even numbers; you can start there.

Answer 2

ok

Answer 3

Factoring out a -1 might also make life easier, but isn't essential..

Answer 4

i know that the -12is taken out like this -12(but cant figure out this part)

Answer 5

hmmm, if you do that, then you'll get a fraction, which will make it more difficult.

Answer 6

(28 is not a multiple of 12)

Answer 7

does this make it a prime polynomial

Answer 8

Nope, it's factorable.

Answer 9

ok but now i am completly lost after reaing the books I thought that is how you do it

Answer 10

Find the GCF of -12, -28, and 24; take that out and you'll be left with a quadratic trinomial that is the product of two linear binomials.

Answer 11

4 i believe

Answer 12

Right, and again, this is just a personal preference because I like my leading coefficients to be positive, but I would take out a -4.

Answer 13

ok then what

Answer 14

\[-12x^2-28x+24=-4(3x^2+7x-6)\]
So keep the -4 on the outside and try to factor the 3x^2+7x-6.
My preferred way is to multiply the leading coefficient (3) by the constant (-6), then find factors of that number that add up to the middle coefficient (7).

Answer 15

That way, you can split the middle term and do factor-by-grouping.

Answer 16

sorry writting this down also to understand it

Answer 17

There are some guess-and-check shortcuts that are sometimes quicker, but this is the general way that works all the time.

Answer 18

Please do. Take your time.

Answer 19

ty

Answer 20

This is a vital skill for algebra. Really understanding this will make a lot of other things a lot easier.

Answer 21

6 *1 =6 but if you do 6+1 =7 so would it be (3x+6)(x+1)

Answer 22

Don't forget that 3 in front of the x^2.
(3x+6)(x+1)=3x^2+9x+6, which is not the trinomial you started with.

Answer 23

nope that does not work when you use the foil system

Answer 24

3 × -6 = -18
Find factors of -18 that add to 7.

Answer 25

9*-2=-18 and 9-2 =7 if that is what you are asking me.

Answer 26

it doesnt work when you foil it using these numbers

Answer 27

do i have the right idea of what I am doing

Answer 28

There is another factoring step, though.
\[3x^2+7x-6=3x^2+9x-2x-6=(3x^2+9x)+(-2x-6)\]
You can factor those two expressions in parentheses separately and find your binomial factors.

Answer 29

You do have the right idea, but there is just a little more breaking apart left to do.

Answer 30

i am not sure what you mean by factoring these two expressions

Answer 31

factor 3x^2+9x and then factor -2x-6

Answer 32

You'll see that both of them have a common binomial factor of (x+3).

Answer 33

ok working on it will be back in a min doing it on paper

Answer 34

In the meantime, here's the guess-and-check method:
To factor 3x^2+7x-6, you know that to get the 3x^2 you need to multiply (3x)(x), and to make the -6, you'll need (-1)(6), (1)(-6), (2)(-3), or (-2)(3). You can test those possibilities by FOILing (3x + __)(x + __)

Answer 35

is it (3x-3)(x+3) and (-2+2)(x+3) still not sure that is right

Answer 36

Almost . . .
\[3x^2+9x=3x(x+3), \space -2x-6=-2(x+3)\]
Factor out the (x+3) and you'll get (x+3)(3x-2).

Answer 37

Don't forget to include the -4 that got factored out at the beginning and you're done.

Answer 38

oh i was doing it wrong ty

Answer 39

how do you write that

Answer 40

ty for your help and being patient with me

Answer 41

And as a taste of things to come, if you had the function
y=-12x^2-28x+24, the X-intercepts of the graph will be at -3 and 2/3
I'll let you figure out why.

Answer 42

lol ok i will try to figure that out