A is the correct answer.
The first term is, z2 its coefficient is 1 .
The middle term is, +z its coefficient is 1 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 1 • -2 = -2
Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is 1 .
-2 + 1 = -1 -1 + 2 = 1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 2
z2 - 1z + 2z - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
z • (z-1)
Add up the last 2 terms, pulling out common factors :
2 • (z-1)
Step-5 : Add up the four terms of step 4 :
(z+2) • (z-1)
Which is the desired factorization
Equation at the end of step 3 : 3 • (z + 2) • (z - 1) = 0
