Rewrite the function by completing the square.
f(x) = x2 + x - 30

1.1     Factoring  x2+x-30 

The first term is,  x2  its coefficient is  1 .

The middle term is,  +x  its coefficient is  1 .

The last term, "the constant", is  -30 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -30 = -30 

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   1 .

     -30   +   1   =   -29     -15   +   2   =   -13     -10   +   3   =   -7     -6   +   5   =   -1     -5   +   6   =   1   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  6 

                     x2 - 5x + 6x - 30

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

                    x • (x-5)

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

                    6 • (x-5)

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

                    (x+6)  •  (x-5)

             Which is the desired factorization

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step-by-step explanation: