Question

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Answer 1

Answer:

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Answer 2

Answer:

Factoring  z2-10z+16 

The first term is,  z2  its coefficient is  1 .

The middle term is,  -10z  its coefficient is  -10 .

The last term, "the constant", is  +16 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 16 = 16 

Step-2 : Find two factors of  16  whose sum equals the coefficient of the middle term, which is   -10 .

     -16   +   -1   =   -17     -8   +   -2   =   -10   That's it

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

                     z2 - 8z - 2z - 16

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

                    z • (z-8)

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

                    2 • (z-8)

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

                    (z-2)  •  (z-8)

             Which is the desired factorization