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anonymous
 one year ago
FACTORING!
please help me factor x^2+3x+9/4
anonymous
 one year ago
FACTORING! please help me factor x^2+3x+9/4

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myininaya
 one year ago
Best ResponseYou've already chosen the best response.1hint: this may help" \[x^2+bx+\frac{c}{a} \\ \frac{1}{a}(ax^2+bax+\frac{c(a)}{a}) \\ \frac{1}{a}(ax^2+bax+c)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so my equation should look like \[1/4(4x^2+3(4)x+9)\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1yep it is like dividing everything by 4 at the same time as multiplying everything by 4 and we know 4/4=1 so yep

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1and 3(4) can be written as 12 of course

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1you can also see if you need to factor anymore

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right, so now my equation should be \[x^2+12+9\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1well you are missing 1/4( ) and a 4 in front of x^2 and a x next to the 12

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{4}(4x^2+12x+9)\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1anyways let's look at the thing in ( )

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1can you find two numbers that multiply to be 4(9)=36 and add up to be 12

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0something that are multiples to 36 and add to 12?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{4}(4x^2+6x+6x+9)\] now we can ignore the 1/4 and bring it down later but we need to factor the thing inside the ( )by grouping

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1we will bring the 1/4 down later \[4x^2+6x+6x+9 \\ (4x^2+6x)+(6x+9) \\ 2x(2x+3)+(6x+9)\] you try factoring the 6x+9

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(6x+9) will equal 3x(2x+3)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1well 9 doesn't have a factor of x so you cannot factor an x out of it unless you divide by x but that is making is nastier than it should be 6x+9=3(2x+3)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1we will bring down 1/4 later \[2x(2x+3)+3(2x+3)\] now one last step

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok, that makes sense!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure how to do the last step

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1example to factor a(b+c)+m(b+c) notice both terms both a(b+c) and m(b+c) have the common factor (b+c) so I can factor (b+c) out of both terms in the sum (b+c)(a+m)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1so you see (2x+3) in both terms the terms being 2x(2x+3) and 3(2x+3)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1what is left of the first term when factoring out the (2x+3) is 2x and of the second term is +3

myininaya
 one year ago
Best ResponseYou've already chosen the best response.12x(2x+3)+3(2x+3) (2x+3)(2x+3)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1don't forget to bring down the 1/4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so its just 1/4(2x+3)(2x+3)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{4}(2x+3)^2 \\ \frac{1}{2^2}(2x+3)^2 \\ \frac{1^2}{2^2}(2x+3)^2 \\ (\frac{1}{2}(2x+3))^2 \\ (\frac{2x+3}{2})^2 \] there is another or :p

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1you could separate the fraction inside the ( )^2

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1but anyways yeah you are done

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so its just \[(x+\frac{ 3 }{ 2 })^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much, I really appreciate your help!

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1if we would have noticed the following to begin with: \[x^2+3x+(\frac{3}{2})^2=(x+\frac{3}{2})^2 \] we wouldn't had so much work

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yes! That's very true, we missed that. Oh well :)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1for example: \[x^2+5x+(\frac{5}{2})^2=(x+\frac{5}{2})^2 \\ x^25x+(\frac{5}{2})^2=(x\frac{5}{2})^2 \\ x^23x+(\frac{3}{2})^2=(x\frac{3}{2})^2 \\ x^22x+(\frac{2}{2})^2=(x1)^2 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that actually makes perfect sense, thank you so much for showing me that formula! It's a lot easier than all the other ways I have been taught.
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