## anonymous one year ago which of the following is a facftor of both x^2 -x-6 and x^2= 5x+6

1. mathstudent55

$$x^2 -x-6$$ First equation $$x^2= 5x+6$$ $$x^2- 5x-6 = 0$$ Second equation

2. 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.

3. mathstudent55

Do you know how to factor those trinomials?

4. anonymous

substracting one line?

5. anonymous

by -1

6. mathstudent55

No. I'll show you.

7. mathstudent55

Here is an example.

8. anonymous

Ok thanks

9. mathstudent55

|dw:1444524163180:dw|

10. 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.

11. mathstudent55

|dw:1444524269218:dw|

12. mathstudent55

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

13. anonymous

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

14. 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

15. 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

16. mathstudent55

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

17. mathstudent55

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

18. mathstudent55

That is how a trinomial of the type $$x^2 + ax + b$$ is factored

19. 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

20. anonymous

thanks I get it :)

21. mathstudent55

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

22. anonymous

Ok thanks @mathstudent55 youre cool :)

23. 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|

24. mathstudent55

|dw:1444524732670:dw|

25. mathstudent55

|dw:1444524792102:dw|

26. anonymous

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

27. 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?

28. mathstudent55

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

29. anonymous

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

30. mathstudent55

|dw:1444525027158:dw|

31. mathstudent55

|dw:1444525062059:dw|

32. mathstudent55

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