Factoring x2-13x+40
The first term is, x2 its coefficient is 1 .
The middle term is, -13x its coefficient is -13 .
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 -13 .
-40 + -1 = -41 -20 + -2 = -22 -10 + -4 = -14 -8 + -5 = -13 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
Final result :
(x - 5) • (x - 8)
