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ganeshie8
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you dont knw how to factor
chocobo907
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2x^2+x-3 factored would be (2x+3)(x-1)
ganeshie8
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you have the answer there. @Christos something u dont understand in how to factor that ?
Christos
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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
ganeshie8
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i understand, let me guide u factor this
Christos
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ty man
ganeshie8
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\(2x^2 + x - 3 \)
ganeshie8
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compare it wid
\(ax^2 + bx + c\)
Christos
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ok
ganeshie8
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we need to pick two numbers whose product equals \(ac\), and sum equals \(b\)
ganeshie8
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a=2
b=1
c=-3
ganeshie8
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can you pick two numbers whose product equals -6, and sum equals 1 ?
surjithayer
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\[2x ^{2}+x-3=2x ^{2}+3x-2x-3\] (2*-3=-6,3-2=1)
\[=x \left( 2x+3 \right)-1\left( 2x+3 \right)=\left( 2x+3 \right)\left( x-1 \right)\]
Christos
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I dont think I can :(
ganeshie8
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tell me what are the factors of -6
Christos
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-1 -2 -3
ganeshie8
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and 1, 2, 3 also
Christos
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ooh ok
ganeshie8
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so, 3 * -2 = -6
ganeshie8
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3 + -2 = 1
ganeshie8
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3 and -2 are our numbers !
Christos
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So we dont take into considaration b ? We just add and multiply a and c?
ganeshie8
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\(2x^2 + x - 3\)
you need to rewrite x as 3x-2x
ganeshie8
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we did consider b, the numbers we pick must multiply to ac, and addup to b
Christos
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"3 * -2 = -6"
"3 + -2 = 1"
Where is b ?
ganeshie8
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we picked 3 and -2, cuz they multiply to ac, and addup to b
ganeshie8
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look at the given expression, b = 1
Christos
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hm the second expression ye
ganeshie8
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\(2x^2 + x - 3\)
can be written as :
\(2x^2 + 1x - 3\)
ganeshie8
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compare it wid ax^2 + bx + c, and tell me whats b ?
Christos
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yea I know it's 1, I just dont know what do it with it :D
Christos
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lol
ganeshie8
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so when you're asking where is b, you knw now that its there, and it is 1 :)
Christos
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from my understanding
we take a*c = whatever it gives
then a+c = whatever it gives
ganeshie8
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not exactly
Christos
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hm
ganeshie8
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we take a*c, tell whats a*c, in our current example ?
Christos
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its -6
ganeshie8
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so we take that -6, and find its factors. that addup to b
ganeshie8
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-6 = 3*-2
Christos
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when you say "add up" what do you mean exactly?
ganeshie8
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when u add both the numbers, you must get b
ganeshie8
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we picked 3 and -2, add them and see if u get b or not
ganeshie8
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if p, q are the two numbers, you should pick them in a way such that :-
pq = ac
p+q = b
ganeshie8
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thats all
Christos
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I see now
ganeshie8
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great :) you do few more problems u wil see more clearly
Christos
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Ok so, we have a*c = -6
a-b = 1
but how do I proceed with this information in hand?
ganeshie8
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heres the full solution, go through
\(2x^2 + x - 3\)
\(2x^2 + 3x - 2x - 3\)
\(x(2x + 3) - 1(2x + 3)\)
\((2x + 3)(x - 1)\)
Christos
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a-c ***
ganeshie8
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no
Christos
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/facepalm I am such a dummy some times, I can see it clearly now, thanks again
ganeshie8
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its,
pq = ac
p+q = b
ganeshie8
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cool all geniuses have few dummy corners ;p
Christos
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yea yea I see, I get you now
Christos
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hihi xP
ganeshie8
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good :)
Christos
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ty dude