Question

Please help me . factor. X^2+18x+77

Answer 1

(x+7)(x+11) is the answer.

Answer 2

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)