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.

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

so the correct answer is (5x+6)(8x-5) ?

can be easily checked by expanding it.

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

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

i totally dropped the ball in this one...i should have definitely know to find x!!!

To solve the equation 40x^2 + 23x - 30 = 0 by finding the numbers that make 30 and add to 23, you can use the method of factoring or splitting the middle term. Here's how you can do it:

Step 1: Multiply the coefficient of the x-square term (40) with the constant term (-30). In this case, it is (-30) × (40) = -1200.

Step 2: Find two numbers that multiply to give -1200 and add up to the coefficient of the x-term (23). These two numbers are 60 and -20 because 60 × -20 = -1200 and 60 + (-20) = 40.

Step 3: Rewrite the middle term (23x) as the sum of the two numbers found in step 2:
40x^2 + 60x - 20x - 30 = 0

Step 4: Group the terms:
(40x^2 + 60x) - (20x + 30) = 0

Step 5: Factor out the common terms from each group:
20x(2x + 3) - 10(2x + 3) = 0

Step 6: Notice that the terms in the parentheses are the same. So, you can factor out the common factor:
(2x + 3)(20x - 10) = 0

Step 7: Set each factor equal to zero and solve for x:
2x + 3 = 0 or 20x - 10 = 0

For the first equation, subtract 3 from both sides:
2x = -3
Divide both sides by 2:
x = -3/2

For the second equation, add 10 to both sides:
20x = 10
Divide both sides by 20:
x = 1/2

So, the solutions to the equation 40x^2 + 23x - 30 = 0 are x = -3/2 and x = 1/2.