Question

factories :z^2-32+256​

Answer 1

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Answer 2

Answer:

The first term is,  z2  its coefficient is  1 .

The middle term is,  -32z  its coefficient is  -32 .

The last term, "the constant", is  +256 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 256 = 256 

Step-2 : Find two factors of  256  whose sum equals the coefficient of the middle term, which is   -32 .

     -256   +   -1   =   -257     -128   +   -2   =   -130     -64   +   -4   =   -68     -32   +   -8   =   -40     -16   +   -16   =   -32   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -16  and  -16 

                     z2 - 16z - 16z - 256

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

                    z • (z-16)

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

                    16 • (z-16)

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

                    (z-16)  •  (z-16)

             Which is the desired factorization