## anonymous one year ago Factoring by groups this quadratic equations -9x^2+13x-4

1. anonymous

check if this right: -9x^2+13x-4 -9x^2+9x+4x-4=0 9x(-x+1) +4(x-1)=0 what am I doing wrong? Why (-x+1) and (x-1) not equal?

2. butterflydreamer

you're close :) take a look here: |dw:1436245778372:dw|

3. anonymous

Thank you very much, you've been very helpful

4. butterflydreamer

you're welcome ^_^!

5. nincompoop

sometimes: $$-1 \times(-9x^2+13x-4)$$ use AC-method $$9 \times 4 = 36$$ identify 2 factors of 36 (AC) that adds to $$|b|$$, (13): yes 9 and 4 $$-1 \times (9x^2 - 9x - 4x +4)$$ $$-1 \times[9x (x-1) -4(x-1)]$$

6. nincompoop
7. anonymous

Why did u multiply by -1?

8. nincompoop

to show you that there are different ways of making use of methods that you can come up with.

9. nincompoop

now let us take it up a notch and treat x-1 as one variable, say p $$-1 [9x(p) - 4(p)] \rightarrow -1(9xp - 4p) \rightarrow -p(9x-4)$$ rewrite: and I will put it back into original by undoing the multiplication of -1 to make you at ease $$-p \rightarrow -1(x-1) = (-x+1)(9x-4)$$ WELCOME to the world of MATH

10. anonymous

I have a another problem: −3x​^2+17x−20 −3x^​2​​+12x+5x−20 (−3x^​2​​+12x)+(5x−20) Is this correct so far.

11. nincompoop

let see what wolframalpha can tell us

12. nincompoop

try the AC method I showed you.

13. nincompoop

look at your coefficients A: B: C: $$3 \times 20 = 60$$ identify two factors of 60 that adds to $$|b|$$ we have 12 and 5

14. nincompoop

this is a test of your arithmetic abilities mostly.

15. anonymous

(−3x^​2​​+12x)+(5x−20) -3x(x-4) +5(x−4) ok why GCF of (−3x^​2​​+12x) is -3x not 3x. Answer: (-3x + 5) ( x - 4)

16. nincompoop

because one is negative, guy

17. nincompoop

you can't escape the negative

18. anonymous

oh alright now I get it. Thanks for your help,sir. i appreciate it

19. nincompoop

do you get the AC-method yet? look at the wolfram alpha attachment I showed you and learn some techniques from it.

20. anonymous

Ac method is similar to factoring by grouping

21. nincompoop

perhaps... perhaps

22. nincompoop

depends on what it involves completing the square, AC-method and quadratic formula they all become handy depending on the problem in chemistry such as in related rates or reaction rates, we use quadratic formula sometimes.

23. anonymous

24. nincompoop

it will depend on the problem you are given

25. anonymous

one last question: -9x^2+9x so the GCF of this binomial is -9x -9x(x-1)

26. butterflydreamer

that would be correct :)