factor 6x^2−3x−9

Question

factor 6x^2−3x−9

janu16 · Answer

$$6x^2-3x-9$$

pooja195 · Answer

here we need to factor by grouping
we start by looking at slandered form : 
$$\huge~\rm~ax^2+bx+c=0$$
From there we deteremine what we need to multiply
|dw:1445393506633:dw|
Looking at that we know that we will multiply
6 x -9 
and 3 is b
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What numbers multiply to make -54 but add/subtract to make -3 ?

janu16 · Answer

-6 times 9 = -54 and -6 subtract 9= 3

janu16 · Answer

do you mean 3 or -3?

pooja195 · Answer

I meant -3 i messed up in the drawing....sorry!

janu16 · Answer

but i dont know how you get -3 with 6 and 9

pooja195 · Answer

Wait i know what I did wrong... 
start over... ignore everything i typed above.

pooja195 · Answer

Can you find a GCF of the numbers 6,3,9, ? 
6x^2−3x−9

janu16 · Answer

3?

janu16 · Answer

3 times 2 =6 3 times 3=9 3 times 3=1

pooja195 · Answer

yes so we divide all the numbers by 3
$$\huge~\rm~ 2x^2-x-3$$

pooja195 · Answer

from here we can factor by grouping.. 
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janu16 · Answer

so far its 6x^2−3x−9
              2x^2-x - 3

janu16 · Answer

so we factor 2x^2-x-3?

pooja195 · Answer

yes

janu16 · Answer

so how do i do it

pooja195 · Answer

What numbers multiply to make -6 but add to make -1

janu16 · Answer

um 2 times -3 = -6 and 2+ -3=-1

pooja195 · Answer

perfect :)  
So now we have 3(2x-6)(2x+1) <---for this one i combined the 2 negs because they made a pos.

pooja195 · Answer

find a to simplfy we can divide 2x-6 both by 2 
so our final answer would be:  3(2x−3)(x+1)

janu16 · Answer

can you like write all the steps out cause I got it but I just want clear picture thanks

pooja195 · Answer

k. gimmie a min...

pooja195 · Answer

find a GCF of the numbers 6,3,9, 
We said 3 
yes so we divide all the numbers by 3
$$\huge~\rm~ 2x^2-x-3$$
We decided that after we factor out the expression we end up with -3 and 2
perfect   
 3(2x-6)(2x+1) <---for this one i combined the 2 negs because they made a pos. 
the 3 at the beginning comes from when we divided all the numbers by 3 in the beginning. 
now we need to make sure the the expression is fully simplified  the gcf of -6 and 2 is 2 right? so we divide and our final answer would be:  3(2x−3)(x+1)

pooja195 · Answer

If you still don't understand please let me know and thank you for the testimonial its sweet :)

janu16 · Answer

when we factored it by 2 and -3 why is the 1 not negative?

pooja195 · Answer

-x means -1.

janu16 · Answer

no right here where you said 3(2x-6)(2x+1) <---for this one i combined the 2 negs because they made a pos.

janu16 · Answer

2x+1 so its not -1? cause 2+-3=-1

pooja195 · Answer

ok 
6x--1 would have been the original equation  
when you have 2 negative signss next to each other it becomes a positive

janu16 · Answer

ohhhok makes sense thanks