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anonymous
 one year ago
How to factor these two functions?
anonymous
 one year ago
How to factor these two functions?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0f(x)=(x3)^2+2 f(x)=4x^2+1615

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't really need the answer. I just need a quick review of how to factor.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know the first one can't be factored.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2is the second one supposed to be f(x)=4x^2+16x15 I put an x after the 16

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I apologize, that was careless of me.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2have you learned the quadratic formula?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you can use the formula to solve 4x^2+16x15 = 0 for x you'll get two roots x = p and x = q you can use those two solutions to find the factorization in the form k*(xp)*(xq) = 0 the k is some fixed number that scales the graph and determines whether the graph opens up or down

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh my gosh. Thank you!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2let me know what you get

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2that's the same as x = 3/2 and x = 5/2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2what we can do is multiply both sides of each equation by 2 x = 3/2 > 3x = 2 x = 5/2 > 5x = 2

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2then move the 2's over through subtraction 3x = 2 > 3x2 = 0 5x = 2 > 5x2 = 0

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2what would come next?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure. I've never seen this done before.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2oh wow I made a big typo I'm just noticing now

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2x = 3/2 should turn into 2x = 3

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2and x = 5/2 should turn into 2x = 5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh. Would you multiply them from there to get the original function?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2ok so through the quadratic formula, we get these 2 solutions x = 3/2, x = 5/2 multiply both sides by 2 2x = 3, 2x = 5 then move everything to one side 2x3=0, 2x5=0

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2we have 2x3=0, 2x5=0 they would turn into (2x3)*(2x5) = 0 I think that's what you had in mind?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2what would (2x3)*(2x5) expand out into?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2that 16 should be negative try again

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2now compare 4x^216x+15 (what you just got when you expanded) with 4x^2+16x15 (the original function). Are they the same? If not, what can we do to make them the same?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't think they are the same. I'm not sure. :[

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would you need a negative one in front of the one I got?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2they aren't the same notice how the 4x^2 is positive in 4x^216x+15 then we have 4x^2 in 4x^2+16x15

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2same for the 16x terms and the 15 terms too

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right. So...what did I do wrong?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Why aren't they the same?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2well to easily fix this, we can stick a 1 in front of the factorization

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2since that will make +4x^2 turn into 4x^2 the 16x turn into +16x and the +15 turn into 15

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2so k = 1 is that constant I was talking about

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh! I think I get it. I understand evrything except the constant. Why is that 1?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Where did the 1 come from?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2if we expanded out (2x3)*(2x5) we end up with 4x^2 as one of the terms we want 4x^2 so we can make (2x3)*(2x5) negative and say 1*(2x3)*(2x5) instead to fix that issue

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2expanding out (2x3)*(2x5) will have 16x but we want +16x that 1 out front fixes the issue

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Understood. Thank you so much, Jim!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you're welcome

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You're the best! Have a good night!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you have a good night as well
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