anonymous
  • anonymous
which of the following is a facftor of both x^2 -x-6 and x^2= 5x+6
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mathstudent55
  • mathstudent55
\(x^2 -x-6\) First equation \(x^2= 5x+6\) \(x^2- 5x-6 = 0\) Second equation
mathstudent55
  • mathstudent55
The first equation can be factored in the form it's given. To factor the second equation, we need it in the form shown in the second line above.
mathstudent55
  • mathstudent55
Do you know how to factor those trinomials?

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anonymous
  • anonymous
substracting one line?
anonymous
  • anonymous
by -1
mathstudent55
  • mathstudent55
No. I'll show you.
mathstudent55
  • mathstudent55
Here is an example.
anonymous
  • anonymous
Ok thanks
mathstudent55
  • mathstudent55
|dw:1444524163180:dw|
mathstudent55
  • mathstudent55
This is a trinomial in which the x^2 term is just x^2. We don't have a number multiplying the x^2.
mathstudent55
  • mathstudent55
|dw:1444524269218:dw|
mathstudent55
  • mathstudent55
You need to find 2 numbers that multiply to -2 and add to -1.
anonymous
  • anonymous
\[\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\] Ax^2+Bx + C
mathstudent55
  • mathstudent55
What are two numbers that multiply to -2? There are two possibilities: -2 and 1 -1 and 2 Notice that both -2 * 1 = -2 and -1 * 2 = -2
mathstudent55
  • mathstudent55
We also need that the two numbers add to -1. -2 + 1 = -1 -1 + 2 = 1 The first line above, -2 and 1 does add to -1. The second line above does not. That means the two numbers we need are -2 and 1
mathstudent55
  • mathstudent55
We set up the factors like this below: |dw:1444524436826:dw|
mathstudent55
  • mathstudent55
Now all we do is place the two numbers we found like this below: |dw:1444524489908:dw|
mathstudent55
  • mathstudent55
That is how a trinomial of the type \(x^2 + ax + b\) is factored
anonymous
  • anonymous
what I wrote is the quadratic formula using your 2 equations x^2 -x-6 and x^2= 5x+6 you can see that for x^2 -x-6 = A = 1 B=-1 C =-6 and for x^2-5x-6 A = 1 B = -5 and C = -6
anonymous
  • anonymous
thanks I get it :)
mathstudent55
  • mathstudent55
Now let's look at the two trinomials you have. \(x^2 -x-6\) First trinomial \(x^2- 5x-6\) Second trinomial
anonymous
  • anonymous
Ok thanks @mathstudent55 youre cool :)
mathstudent55
  • mathstudent55
Since both of these trinomials have a plain x^2 term (with a coefficient of 1), we can factor them easily. We set them up like this: |dw:1444524646962:dw|
mathstudent55
  • mathstudent55
|dw:1444524732670:dw|
mathstudent55
  • mathstudent55
|dw:1444524792102:dw|
anonymous
  • anonymous
-3 x 2 for the first one and -3 x -2 for second
mathstudent55
  • mathstudent55
You are correct for the first one. The second has a mistake. When you wrote the original post, I think you wrote an = when you meant to write a +. Is that correct?
mathstudent55
  • mathstudent55
Should the second trinomial be x^2 + 5x + 6 ? Your equal sign instead of the first plus sign is a typo?
anonymous
  • anonymous
@mathstudent55 is right, if you didn't make a typo something is off.
mathstudent55
  • mathstudent55
|dw:1444525027158:dw|
mathstudent55
  • mathstudent55
|dw:1444525062059:dw|
mathstudent55
  • mathstudent55
Which factor is in common? |dw:1444525083439:dw|