The first term is, 3p2 its coefficient is 3 .
The middle term is, -2p its coefficient is -2 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 3 • -5 = -15
Step-2 : Find two factors of -15 whose sum equals the coefficient of the middle term, which is -2 .
-15 + 1 = -14 -5 + 3 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 3
3p2 - 5p + 3p - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (3p-5)
Add up the last 2 terms, pulling out common factors :
1 • (3p-5)
Step-5 : Add up the four terms of step 4 :
(p+1) • (3p-5)
Which is the desired factorization
Final result : (3p - 5) • (p + 1)
