A is the correct answer.
The first term is, <span> <span>z2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> +z </span> its coefficient is <span> 1 </span>.
The last term, "the constant", is <span> -2 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 1</span> • -2 = -2</span>
Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is <span> 1 </span>.
<span><span> -2 + 1 = -1</span><span> -1 + 2 = 1 That's it</span></span>
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 2
<span>z2 - 1z</span> + 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
<span>Equation at the end of step 3 :</span><span> 3 • (z + 2) • (z - 1) = 0 </span>
