The first term is, x2 its coefficient is 1 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -40
Step-1 : Multiply the coefficient of the first term by the constant 1 • -40 = -40
Step-2 : Find two factors of -40 whose sum equals the coefficient of the middle term, which is -3 .
-40 + 1 = -39
-20 + 2 = -18
-10 + 4 = -6
-8 + 5 = -3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 5
x2 - 8x + 5x - 40
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-8)
Add up the last 2 terms, pulling out common factors :
5 • (x-8)
Step-5 : Add up the four terms of step 4 :
(x+5) • (x-8)
Which is the desired factorization
Answer: 6 • ( x + 5 ) • ( x - 8 )
