## AshhSmith 3 years ago a^2 – a – 20 factor completely

1. vishweshshrimali5

\[a^2 - a - 20 = a^2 - 5a + 4a - 20\] Now u can simplify this

2. agentx5

Hint: -5 and +4 ;-) Got it now?

3. Callisto

From @vishweshshrimali5 's work: a^2 - a - 20 = a^2 - 5a + 4a - 20 = a (a-5) + 4(a-5) = (a+4)(a-5) If you have to solve the quad. equation, that's another case.

4. agentx5

a^2-a-20=(a-5)(a+4) I stand by what I said. -5 + 4 = -1 -5 * 4 = -20

5. agentx5

So no, not wrong answer. Dude.

6. AshhSmith

thank you guys

7. Callisto

Sorry @vishweshshrimali5 I think you're more like solving the quadratic equation than just factor the expression. Please look at the question again

8. vishweshshrimali5

@Callisto very correct I regret for my mistake We just had to factorise right ?

9. Callisto

Root is negative of the number in the factor. I'm 100% sure that @agentx5 is correct!

10. agentx5

I'm not using the quadratic. I'm doing it in my head by considering what would have to come back together to for a^2-a-20 when I F.O.I.L. the factors together.

11. Callisto

Yes @vishweshshrimali5

12. Callisto

@vishweshshrimali5 You shouldn't be sorry. Instead we are so sorry to tell you that the question is *factor completely*

13. agentx5

Neither Callisto nor I have forgotten, this is just a method that works easier and faster in this situation as a method to factor, and just as correct. Roots implies an EQUATION, not an EXPRESSION.

14. agentx5

There is no '=' in the original question.

15. Callisto

@vishweshshrimali5 No. If it is the quadratic equation. It is solve like this: a^2 – a – 20 =0 (a-5)(a+4) =0 a-5 =0 or a+4 =0 a=5 or a=-4

16. Callisto

@vishweshshrimali5 I've posted the way to do it

17. AshhSmith

can you factor a^2 – 5a – 20 out for me ?

18. vishweshshrimali5

@Callisto I think I have misunderstood u all Sorry for that

19. vishweshshrimali5

What @agentx5 was saying were not roots right ? u were telling how to write -x = -5x + 4x right ? Sorry everyone I regret for my words

20. Callisto

It's okay. Is that clear to you now? @vishweshshrimali5

21. agentx5

But then again there was NO f(a)=0 equation, it was simply an expression. @AshhSmith , Callisto and I both did that (see above) :-)

22. vishweshshrimali5

If I m not wrong @Callisto told the way to factorise @agentx5 told how to write -x = -5x + 4x and I told how to solve the quadratic eq. Sorry everyone Please don't mind that

23. Callisto

@AshhSmith First, please post it as a new question. Second, I'm sure we're all glad to help, provided that you've tried to work out the answer first - no matter you succeed or not. Third, in response to your question, if you need to form (ax+b)(cx+d) where a, b, c, and d are integers, then it can't be factored in the case x^2-5x-20.

24. Callisto

@vishweshshrimali5 I hope I can explain it clearly to you... First it's about 'factor completely' Factor completely is about factoring the expression. The expression given in the question is x^2 -x - 20 So, we have to factor it. x^2 - x -20 = x^2 - 5x + 4x - 20 = x (x-5) + 4(x-5) = (x-5)(x+4) This is what factor completely is, and nothing more. What you've been talking about is solve the equation. And the way you've been working is to use some properties of quadratic equation to work out the roots ( that is the value of the unknowns) of the quadratic equation. With the word ''equation'', that means there are TWO sides and a equal sign in between (that is '=') and you need to SOLVE it. For example : x^2 -x - 20 = 0 -> you can see there are TWO sides separated by an equal sign. To solve it. One of the techniques is to factor it. That is x^2 -x - 20 = 0 (x-5)(x+4) = 0 Since two factors multiply to give 0, one of them must be 0. So, (x-5) =0 or (x+4) =0 x = 5 or x = -4 This is solving the equation/ solve x/ find the roots of the equation, but NOT factor the expression. I hope it's clearer to you now.