inowalst
  • inowalst
The quadratic expressions \(x^2+5x−14\) and \(49-x^2\)​​ share a common binomial factor.
Mathematics
katieb
  • katieb
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YanaSidlinskiy
  • YanaSidlinskiy
So, what's the question? Are we supposed to factor it out?
ParthKohli
  • ParthKohli
They do.
inowalst
  • inowalst
Yes. @YanaSidlinskiy I need help doing that.

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welshfella
  • welshfella
first take x out of the quadratic function
inowalst
  • inowalst
But one is negative and one isn't..
welshfella
  • welshfella
oh sorry you can simplify first (x^2+5x−14x^2 = 5x - 13x^2 = x(5 - 13x)
welshfella
  • welshfella
there are no common factors here are you sure you have the question right?
inowalst
  • inowalst
The 14 isn't supposed to have \(x^2\)
welshfella
  • welshfella
i suspect thet the quadratic is x^2+5x−14
welshfella
  • welshfella
right
inowalst
  • inowalst
Sorry about that.
welshfella
  • welshfella
to factor x^2+5x−14 you need to find 2 numbers whose product is -14 and whose sum is +5
welshfella
  • welshfella
can you tell me what those 2 numbers sre?
welshfella
  • welshfella
think of the factors of -14
inowalst
  • inowalst
Their product has to be -14 but the sum has to be 5?
welshfella
  • welshfella
yes
inowalst
  • inowalst
Hm.. I don't really know, but I know for the -14..
welshfella
  • welshfella
-14 = -7 * 2 or -14 = -2 * 7
welshfella
  • welshfella
which 2 factors add up to +5?
inowalst
  • inowalst
-2+7
welshfella
  • welshfella
right on so the factors of (x^2+5x−14) are ( x - 7)(x + 2)
welshfella
  • welshfella
if you expand this function you'll see it works out to x^2 + 5x - 14
welshfella
  • welshfella
* oops my bad its (x + 7)(x - 2)
inowalst
  • inowalst
Yes. Thank you so much.
welshfella
  • welshfella
Now you need to factor x^2 - 49
inowalst
  • inowalst
Okay.
welshfella
  • welshfella
can u do that?
welshfella
  • welshfella
49 - x^2
inowalst
  • inowalst
(x-7)(x+7) ? I don't know..
welshfella
  • welshfella
49 - x^2 = (7 - x)(7 + x) so can you see the common factor?
inowalst
  • inowalst
Yes.
welshfella
  • welshfella
x + 7
inowalst
  • inowalst
Oh, okay. Thanks a bunch.

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