Question

Factored form of x^2+15x+56

Answer 1

Answer:

(x + 8) • (x + 7)

Step-by-step explanation:

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  x2+15x+56

The first term is,  x2  its coefficient is  1 .

The middle term is,  +15x  its coefficient is  15 .

The last term, "the constant", is  +56

Step-1 : Multiply the coefficient of the first term by the constant   1 • 56 = 56

Step-2 : Find two factors of  56  whose sum equals the coefficient of the middle term, which is   15 .

     -56    +    -1    =    -57

     -28    +    -2    =    -30

     -14    +    -4    =    -18

     -8    +    -7    =    -15

     -7    +    -8    =    -15

     -4    +    -14    =    -18

     -2    +    -28    =    -30

     -1    +    -56    =    -57

     1    +    56    =    57

     2    +    28    =    30

     4    +    14    =    18

     7    +    8    =    15    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  7  and  8

                    x2 + 7x + 8x + 56

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 :

                   8 • (x+7)

Step-5 : Add up the four terms of step 4 :

                   (x+8)  •  (x+7)

            Which is the desired factorization

Final result :

 (x + 8) • (x + 7)

Processing ends successfully

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