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Factor this

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you dont knw how to factor
2x^2+x-3 factored would be (2x+3)(x-1)
you have the answer there. @Christos something u dont understand in how to factor that ?

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@ganeshie8 certainly I don't understand how I should start? Will you guys be willing to show me the first step? Thee are certain expressions that just dont ring a bell on me, it's not that I cant factor, just some specific ones
i understand, let me guide u factor this
ty man
\(2x^2 + x - 3 \)
compare it wid \(ax^2 + bx + c\)
we need to pick two numbers whose product equals \(ac\), and sum equals \(b\)
a=2 b=1 c=-3
can you pick two numbers whose product equals -6, and sum equals 1 ?
\[2x ^{2}+x-3=2x ^{2}+3x-2x-3\] (2*-3=-6,3-2=1) \[=x \left( 2x+3 \right)-1\left( 2x+3 \right)=\left( 2x+3 \right)\left( x-1 \right)\]
I dont think I can :(
tell me what are the factors of -6
-1 -2 -3
and 1, 2, 3 also
ooh ok
so, 3 * -2 = -6
3 + -2 = 1
3 and -2 are our numbers !
So we dont take into considaration b ? We just add and multiply a and c?
\(2x^2 + x - 3\) you need to rewrite x as 3x-2x
we did consider b, the numbers we pick must multiply to ac, and addup to b
"3 * -2 = -6" "3 + -2 = 1" Where is b ?
we picked 3 and -2, cuz they multiply to ac, and addup to b
look at the given expression, b = 1
hm the second expression ye
\(2x^2 + x - 3\) can be written as : \(2x^2 + 1x - 3\)
compare it wid ax^2 + bx + c, and tell me whats b ?
yea I know it's 1, I just dont know what do it with it :D
so when you're asking where is b, you knw now that its there, and it is 1 :)
from my understanding we take a*c = whatever it gives then a+c = whatever it gives
not exactly
we take a*c, tell whats a*c, in our current example ?
its -6
so we take that -6, and find its factors. that addup to b
-6 = 3*-2
when you say "add up" what do you mean exactly?
when u add both the numbers, you must get b
we picked 3 and -2, add them and see if u get b or not
if p, q are the two numbers, you should pick them in a way such that :- pq = ac p+q = b
thats all
I see now
great :) you do few more problems u wil see more clearly
Ok so, we have a*c = -6 a-b = 1 but how do I proceed with this information in hand?
heres the full solution, go through \(2x^2 + x - 3\) \(2x^2 + 3x - 2x - 3\) \(x(2x + 3) - 1(2x + 3)\) \((2x + 3)(x - 1)\)
a-c ***
/facepalm I am such a dummy some times, I can see it clearly now, thanks again
its, pq = ac p+q = b
cool all geniuses have few dummy corners ;p
yea yea I see, I get you now
hihi xP
good :)
ty dude

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