actoring x2+18x+77
The first term is, x2 its coefficient is 1 .
The middle term is, +18x its coefficient is 18 .
The last term, "the constant", is +77
Step-1 : Multiply the coefficient of the first term by the constant 1 • 77 = 77
Step-2 : Find two factors of 77 whose sum equals the coefficient of the middle term, which is 18 .
-77 + -1 = -78 -11 + -7 = -18 -7 + -11 = -18 -1 + -77 = -78 1 + 77 = 78 7 + 11 = 18 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 7 and 11
x2 + 7x + 11x + 77
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+7)
Add up the last 2 terms, pulling out common factors :
11 • (x+7)
Step-5 : Add up the four terms of step 4 :
(x+11) • (x+7)
Which is the desired factorization
Final result :
(x + 11) • (x + 7)
