Final answer:
The polynomial p(x) = x(x - 3)(2 + 6) simplifies to p(x) = x(x - 3) × 8. The zeros/solutions of the polynomial are the values of x that make p(x) equal to zero, which are 0 and 3.
Step-by-step explanation:
To find the zeros/solutions of the given polynomial in factored form p(x) = x(x - 3)(2 + 6), we first simplify the constants in the factored form. The constant factors of 2 and 6 add up to 8, so the polynomial simplifies to p(x) = x(x - 3) × 8. To find the zeros, we set the polynomial equal to zero and solve for x. The zeros are the values of x that make the polynomial equal to zero.
Thus, solving for x, we have:
- x=0
- x - 3 = 0 => x = 3
The polynomial p(x) will be equal to zero when x is 0 or 3. Therefore, the zeros/solutions of the polynomial p(x) are 0 and 3.