Solve z^2-2z-35=0 using zero product

z = 7 or z=-5

Step-by-step explanation:

First you need to factor the polynomial.

To factor  - 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,

- 7z + 5z - 35  = 0   factor the left by grouping

( -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  

because that’s us why