1. The problem asks for the number of zeros of the polynomial function $$y = (x - 8)(x + 3)^2$$. 2. The zeros of a polynomial are the values of $x$ that make $y=0$. 3. To find zeros, set the function equal to zero: $$ (x - 8)(x + 3)^2 = 0 $$ 4. Use the zero product property: if a product of factors equals zero, then at least one factor must be zero. 5. Set each factor equal to zero: $$ x - 8 = 0 \implies x = 8 $$ $$ (x + 3)^2 = 0 \implies x + 3 = 0 \implies x = -3 $$ 6. The zeros are $x=8$ and $x=-3$. 7. Note that $x=-3$ is a zero of multiplicity 2 because of the squared factor. 8. The number of distinct zeros is 2. Final answer: C. 3 is incorrect; the correct choice is D. 2 zeros.