Final answer:
The zeros of the polynomial f(x)=x³+9x²+23x+15 are -1, -3, and -5.
Step-by-step explanation:
The zeros of the polynomial f(x)=x³+9x²+23x+15 can be found by factoring or using the Rational Root Theorem. To find the zeros of the polynomial, we can use synthetic division or long division to divide the polynomial by a binomial. Let's try dividing by (x+1), and if we get a remainder of 0, then -1 is a zero of the polynomial. By dividing, we find that the remainder is 0, so x = -1 is one of the zeros. We can then use polynomial long division or synthetic division to divide the polynomial by (x+1), and we end up with a quadratic equation, which we can solve for the remaining zeros:
x³+9x²+23x+15 = (x+1)(x²+8x+15) = (x+1)(x+3)(x+5)
So the zeros of the polynomial f(x)=x³+9x²+23x+15 are -1, -3, and -5.