Factoring x2+2x-35
The first term is, x2 its coefficient is 1 .
The middle term is, +2x its coefficient is 2 .
The last term, "the constant", is -35
Step-1 : Multiply the coefficient of the first term by the constant 1 • -35 = -35
Step-2 : Find two factors of -35 whose sum equals the coefficient of the middle term, which is 2 .
-35 + 1 = -34 -7 + 5 = -2 -5 + 7 = 2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 7
x2 - 5x + 7x - 35
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
7 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x+7) • (x-5)
Which is the desired factorization
Final result : (x + 7) • (x - 5)