## bridgetolivares 3 years ago Explain, in complete sentences, how you would completely factor 20x2 – 28x – 48 by using the grouping method. How would you check your factors for accuracy?

1. bahrom7893

I don't wanna write an essay... I can solve, not explain..

2. bridgetolivares

that would be fine too.

3. UnkleRhaukus

4(5x-12)(x+1)

you pull out the GCF first (which is 4), when you factor the trinomial. You can check you're answer by plugging in values for x... a nice value to use is like 1.

6. bridgetolivares

Thank you

np :)

8. mathg8

bahroom - being able to explain a concept demonstrates the mastery ...

9. mathg8

bridget - I'm a math teacher. Can you explain how to factor 5x^2 -7x -12 into (5x-12)(x+1) ? hint : there is an almost exact method for factoring trinomials with leading coefficients different than 1 !

10. bahrom7893

mathg, LE CHALLENGE ACCEPTED (One O in my name)

11. bahrom7893

Explain, in complete sentences, how you would completely factor 20x2 – 28x – 48 by using the grouping method. Okay, group like terms, usually like terms are the ones that have factors or coefficients in common

12. bahrom7893

Pull out a 4 from the whole thing: 4(5x^2 - 7x - 6).. factor 5x^2 - 7x - 6 further, i never learned that shortcut where factors of something add up to something, so I've always used this brute force method (discriminant :) ) D = b^2-4ac = (-7)^2 - 4 * 5 * (-6) = 49 + 120 = 169 x1 = (-b-sqrt(D))/(2a) = (-(-7)-sqrt(169))/(2*5) = (7 - 13)/10 = -6/10 = -3/5 x2 = (-b+sqrt(D))/(2a) = (-(-7)+sqrt(169))/(2*5) = (7 + 13)/10 = 20/10 = 2 Factors: (x-x1)(x-x2)

13. bahrom7893

So your equation factored becomes: 4(x-(-3/5))(x-2) or 4(x+(3/5))(x-2)

14. mathg8

Ok ... bahroom I have a different method ... faster , I think .

15. mathg8

find the product of the leading coefficient and the free term (a*c), in our case (5)*(-12)=-60 , b the coefficient of x is the sum (-7) . The task is to find two factors of (-60) that add up to (-7). After a bit of mental trial and error we can see the two factors we're looking for are -12 and 5 . Now rewrite the trinomial substituting -7x with -12x + 5x. 5x^2 +5x - 12x -12 - Factor by grouping : 5x(x+1)-12(x+1) and factor again the GCF (x+1)(5x-12) . QED

16. bahrom7893

One O in my name

17. bahrom7893

I thought math teachers paid attention to details

18. mathg8

19. mathg8

the 4(-6) ≠ -48

20. bahrom7893

yes i did, tnx for letting me know