Answer: z = 7 or z=-5
Step-by-step explanation:
First you need to factor the polynomial.
To factor [tex]z^{2}[/tex] - 2z -35 You will need to find two numbers that their product is -35 and their sum is -2 and the numbers -7 and 5 works out.
Rewrite the polynomial as,
[tex]z^{2}[/tex] - 7z + 5z - 35 = 0 factor the left by grouping
([tex]z^{2}[/tex] -7z) (5z -35) = 0
z(z -7) 5(z - 7) = 0 Factor out z-7
(z-7)(z+5) = 0 Now apply the zero product by setting each of them equal 0.
z-7= 0 or z+5=0
+7 +7 -5 -5
z = 7 or z= -5
