Question

x^2+38x+961 middle term split​

Answer 1

Answer:

Step-by-step explanation:

Step by step solution :

STEP

1

:

Equation at the end of step 1

 (31x2 -  38x) +  7  = 0  

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  31x2-38x+7  

The first term is,  31x2  its coefficient is  31 .

The middle term is,  -38x  its coefficient is  -38 .

The last term, "the constant", is  +7  

Step-1 : Multiply the coefficient of the first term by the constant   31 • 7 = 217  

Step-2 : Find two factors of  217  whose sum equals the coefficient of the middle term, which is   -38 .

     -217    +    -1    =    -218  

     -31    +    -7    =    -38    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -31  and  -7  

                    31x2 - 31x - 7x - 7

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

                   31x • (x-1)

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

                   7 • (x-1)

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

                   (31x-7)  •  (x-1)

            Which is the desired factorization