Factor completely: 6x^2-4x-2

- anonymous

Factor completely: 6x^2-4x-2

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- DanJS

take a 2 out first.
2*(3x^2 - 2x - 1)

- anonymous

okay i did that, then i did 2(3x-3x)(x-1)

- DanJS

you have factors
3 1 --- 1 1
you need to make a -2 out of that , so +3 and -1

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- anonymous

explain i dont get it

- DanJS

Here you can put in the x terms since 3 and 1 are the only choice
2*(3x )*(x )

- DanJS

and the other choice is only 1 and 1 for the others, you just have to decide the sign in each one + or -

- DanJS

2*(3x 1 )*(x 1)

- DanJS

put in the + or - , so that when you distribute that, you get a -2 on the X term

- anonymous

i already put the x terms in as 2(3x-3x)(x-1)

- anonymous

what do i do next

- welshfella

2*(3x^2 - 2x - 1)
= 2( 3x^2 - 3x + x - 1)
now factor the expression in the parentheses by grouping

- welshfella

first factor 3x^2 - 3x
- take 3x out

- anonymous

so add 3 to both sides?

- triciaal

|dw:1438815014897:dw|

- welshfella

no we are not solving an equation
3x^2 - 3x = 3x(x - 1)
do you get that?

- welshfella

3x is the highest common factor of 3x^2 and 3x

- anonymous

oh so its not 2(3x^2-3x) + (x-1)

- welshfella

well thats on the way to solving it
but we need to factor the first 2 terms first - the 3x^2 - 3x

- welshfella

2(3x^2-3x) + (x-1)
= 2 ( 3x( x - 1) + 1(x - 1) )
now as (x - 1) is common to the 2 parts
= 2 (3x + 1)(x - 1)

- welshfella

- thats whats called factoring by grouping - grouping the first 2 terms and the last 2

- anonymous

wait so what happened to the 3x^2

- welshfella

its was split into 3x and x
3x(x - 1)

- welshfella

- that called factroing

- anonymous

oh so its still 3x^2. so why did you multiply x-1 on both sides

- anonymous

oh wait you didnt

- welshfella

because (x - 1) is common to both parts :-
3x( x - 1) + 1(x - 1)

- anonymous

how?

- welshfella

well its like
Ax - A b
- you can take A out and the factors are
A ( x - b)
if A had been (x - 1) we would take (x - 1) out in a similar way

- welshfella

do you see the pattern there?

- anonymous

so b is -2

- welshfella

??

- welshfella

no that was an example of factoring b is just b i could have put any letter i liked there

- welshfella

i was illustrating how you can take out common items for an expression in order to factor them What goes in the brackets is what is left after taking out the common item.

- welshfella

* from an expression

- anonymous

oh okay so the final result is 2(3x+1)-(x-1)

- anonymous

oh okay i got how you got 2(3x+1)-(x-1)

- welshfella

no there's no - there
the 3 parts multiply each other
its
2(2x +1(x - 1)

- welshfella

gtg
its getting late in the UK

- anonymous

okay thank u

- welshfella

yw

- welshfella

I hate MOndays too!!

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