Posted by **lynne** on Monday, November 1, 2010 at 10:11pm.

question is 40x^2 + 23x -30 = 0

reads as 40x squared plus 23x minus 30 equals zero...please help, we have not learned the quadric formula yet so we are finding the numbers that make 30 and add to 23.

- math -
**Reiny**, Monday, November 1, 2010 at 10:42pm
I use a method that nobody seems to either teach or learn anymore, yet it is the fastest way to find the factors if they exist

I make a pair of two columns, one for the factors of 40, another for the factors of 30

(they line up vertically)

2 4 5 -------2 3 5 15 10 6

20 10 8 ----15 10 6 2 3 5

I then form cross-products with a column pair from the first and a column pair from the second

In this case I am looking for a difference of 23, since the last term is -30

Had it been +30 I would look for a sum of 23

I notice my pairs

5 --- 6

8 --- 5

give the cross-product difference of 5x5 - 6x8 = -23

so my factors must be

(5x .....6)(8x .... 5)

A quick mental check gives me

(5x+6)(8x-5)

Notice I repeat the factors in one of the groups by flipping the order. Most of the time I don't list all the combinations, often skipping the extreme ones like

1

40

In actual practise it only took me about 30 seconds to find the above

- math -
**lynne**, Monday, November 1, 2010 at 10:58pm
so the correct answer is (5x+6)(8x-5) ?

- math -
**Reiny**, Monday, November 1, 2010 at 11:17pm
can be easily checked by expanding it.

- math -
**lynne**, Monday, November 1, 2010 at 11:23pm
i did and came up with the same. however when i entered it they said it was wrong, s/b X= 5/8, -6/5...not sure how

- math -
**Reiny**, Tuesday, November 2, 2010 at 7:43am
Since the hard part was to factor it, I assumed that you would finish it.

so

(5x+6)(8x-5) = 0

x = -6/5 or x = 5/8

- math -
**Lynne**, Tuesday, November 2, 2010 at 5:54pm
i totally dropped the ball in this one...i should have definitely know to find x!!!

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