anonymous
  • anonymous
Factor the Polynomial Completely; X to the third, minus 2xsquared, - 24x Please Help Thanks!!!
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mathstudent55
  • mathstudent55
How about using math symbols for math? It'll make it much easier to read.
mathstudent55
  • mathstudent55
You can write it like this x^3 - 2x^2 - 24x, or even better like this \(x^3 - 2x^2 - 24x\)
anonymous
  • anonymous
How do I do that???

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mathstudent55
  • mathstudent55
Did I understand the expression correctly?
anonymous
  • anonymous
Yes
mathstudent55
  • mathstudent55
The first one is simply typing on your keyboard. The second uses the Equation Editor (blue box below), or writing in Latex.
mathstudent55
  • mathstudent55
Ok. Let's get to your problem.
mathstudent55
  • mathstudent55
The first step in factoring an expression is to look for a common factor. Look at each term. Look at both the coefficients (the numbers) and the variables. Is there a common factor that can be factored out?
anonymous
  • anonymous
|dw:1449448804446:dw| That is what I go t I am not sure how to simplify after that
mathstudent55
  • mathstudent55
Good. That is what I meant. You pulled out a common factor of x. That is a good start.
anonymous
  • anonymous
What should I do next?
anonymous
  • anonymous
Is the common factor 2 b/c 2 divided by 24 is 12??
anonymous
  • anonymous
|dw:1449449014597:dw| The blank spot are the spots I am not sure about
mathstudent55
  • mathstudent55
Now you have a trinomial to factor. Your trinomial is \(x^2 - 2x - 24\) As you can see, the coefficient of the \(x^2\) term is 1. That is called the leading coefficient. To factor a square trinomial with a leading coefficient of 1 1, all you need to do is come up with 2 numbers that multiply to the last coefficient and add to the middle coefficient. You need 2 numbers that multiply to -24 and add to -2.
anonymous
  • anonymous
Only -2 goes into and -24
anonymous
  • anonymous
How can 12*2 (=24) Add to Two????
mathstudent55
  • mathstudent55
|dw:1449449071271:dw|
anonymous
  • anonymous
|dw:1449449240815:dw| Is that correct?
mathstudent55
  • mathstudent55
-24 = -1 * 24 -24 = -24 * 1 -24 = -2 * 12 -24 = -12 * 2 -24 = -3 * 8 -24 = -8 * 3 -24 = -4 * 6 -24 = -6 * 4 As you can see, there are 8 different pairs of numbers that multiply to -24. How many of those pairs of numbers add to -2?
anonymous
  • anonymous
-6+4!
anonymous
  • anonymous
|dw:1449449384494:dw|
mathstudent55
  • mathstudent55
What you did above in incorrect for two reasons. The numbers -2 and -12 multiply to POSITIVE 24, not -24. Also, -2 and -12 do not add to -2.
mathstudent55
  • mathstudent55
Correct. The numbers are -6 and 4.
anonymous
  • anonymous
Thanks SO SOSOOSOSOSO MUCH!!!!
mathstudent55
  • mathstudent55
You're welcome. Remember what you learned here. 1. To factor an expression always start by trying to factor a common factor out of all terms. 2. To factor a square trinomial with a leading coefficient of 1, all you need is to find two numbers that multiply to the third coefficient and add to the middle coefficient. 3. Then the factorization is (x - one number) (x - the other number)
anonymous
  • anonymous
Thanks I will remember that as I finish my math set!
mathstudent55
  • mathstudent55
Great.

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