Question

Find all the zeros of the function
f(x)= (x+5)(x-8)^2

Answer 1

the (only) values for which f(x) is zero is when (x+5) is zero or when (x-8) is zero; since zero time anything is zero.

equations x + 5 = 0 and x - 8 = 0 will find both zeros

Answer 2

Since (x+5) and (x-8) are the two factors of this polynomial
therefore (x+5) = 0 and (x-8) =0
i.e. x=-5 and x=8 are the two zeroes of the given polynomial.