which of the following is a facftor of both x^2 -x-6 and x^2= 5x+6

- anonymous

which of the following is a facftor of both x^2 -x-6 and x^2= 5x+6

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- mathstudent55

\(x^2 -x-6\) First equation
\(x^2= 5x+6\)
\(x^2- 5x-6 = 0\) Second equation

- 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

Do you know how to factor those trinomials?

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## More answers

- anonymous

substracting one line?

- anonymous

by -1

- mathstudent55

No. I'll show you.

- mathstudent55

Here is an example.

- anonymous

Ok thanks

- mathstudent55

|dw:1444524163180:dw|

- 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

|dw:1444524269218:dw|

- mathstudent55

You need to find 2 numbers that multiply to -2 and add to -1.

- anonymous

\[\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\] Ax^2+Bx + C

- 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

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

We set up the factors like this below:
|dw:1444524436826:dw|

- mathstudent55

Now all we do is place the two numbers we found like this below:
|dw:1444524489908:dw|

- mathstudent55

That is how a trinomial of the type
\(x^2 + ax + b\) is factored

- 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

thanks I get it :)

- mathstudent55

Now let's look at the two trinomials you have.
\(x^2 -x-6\) First trinomial
\(x^2- 5x-6\) Second trinomial

- anonymous

Ok thanks @mathstudent55 youre cool :)

- 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

|dw:1444524732670:dw|

- mathstudent55

|dw:1444524792102:dw|

- anonymous

-3 x 2 for the first one and -3 x -2 for second

- 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

Should the second trinomial be
x^2 + 5x + 6 ?
Your equal sign instead of the first plus sign is a typo?

- anonymous

@mathstudent55 is right, if you didn't make a typo something is off.

- mathstudent55

|dw:1444525027158:dw|

- mathstudent55

|dw:1444525062059:dw|

- mathstudent55

Which factor is in common?
|dw:1444525083439:dw|