Answer:

Step by Step Solution

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STEP

1

:

Trying to factor by splitting the middle term

1.1     FACTORING  A2+8a+15

The first term is,  a2  its coefficient is  1 .

The middle term is,  +8a  its coefficient is  8 .

The last term, "the constant", is  +15

Step-1 : Multiply the coefficient of the first term by the constant   1 • 15 = 15

Step-2 : Find two factors of  15  whose sum equals the coefficient of the middle term, which is   8 .

     -15    +    -1    =    -16

     -5    +    -3    =    -8

     -3    +    -5    =    -8

     -1    +    -15    =    -16

     1    +    15    =    16

     3    +    5    =    8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  3  and  5

                    a2 + 3a + 5a + 15

Step-4 : Add up the first 2 terms, pulling out like factors :

                   a • (a+3)

             Add up the last 2 terms, pulling out common factors :

                   5 • (a+3)

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

                   (a+5)  •  (a+3)

            Which is the DESIRED factorization

Final result :

 (a + 5) • (a + 3)

Step-by-step explanation: