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take a 2 out first. 2*(3x^2 - 2x - 1)
okay i did that, then i did 2(3x-3x)(x-1)
you have factors 3 1 --- 1 1 you need to make a -2 out of that , so +3 and -1
explain i dont get it
Here you can put in the x terms since 3 and 1 are the only choice 2*(3x )*(x )
and the other choice is only 1 and 1 for the others, you just have to decide the sign in each one + or -
2*(3x 1 )*(x 1)
put in the + or - , so that when you distribute that, you get a -2 on the X term
i already put the x terms in as 2(3x-3x)(x-1)
what do i do next
2*(3x^2 - 2x - 1) = 2( 3x^2 - 3x + x - 1) now factor the expression in the parentheses by grouping
first factor 3x^2 - 3x - take 3x out
so add 3 to both sides?
no we are not solving an equation 3x^2 - 3x = 3x(x - 1) do you get that?
3x is the highest common factor of 3x^2 and 3x
oh so its not 2(3x^2-3x) + (x-1)
well thats on the way to solving it but we need to factor the first 2 terms first - the 3x^2 - 3x
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)
- thats whats called factoring by grouping - grouping the first 2 terms and the last 2
wait so what happened to the 3x^2
its was split into 3x and x 3x(x - 1)
- that called factroing
oh so its still 3x^2. so why did you multiply x-1 on both sides
oh wait you didnt
because (x - 1) is common to both parts :- 3x( x - 1) + 1(x - 1)
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
do you see the pattern there?
so b is -2
no that was an example of factoring b is just b i could have put any letter i liked there
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.
* from an expression
oh okay so the final result is 2(3x+1)-(x-1)
oh okay i got how you got 2(3x+1)-(x-1)
no there's no - there the 3 parts multiply each other its 2(2x +1(x - 1)
gtg its getting late in the UK
okay thank u
I hate MOndays too!!