For the polynomial below, 3 is a zero.
\[
g(x)=x^{3}+2 x^{2}-9 x-18
\]

Answer

Expert–verified

Hide Steps

Answer

Final Answer: \(\boxed{0}\)

Steps

Step 1 ：The given polynomial is \(g(x)=x^{3}+2 x^{2}-9 x-18\).

Step 2 ：It is stated that 3 is a zero of the polynomial. This means that if we substitute x = 3 into the polynomial, the result should be zero.

Step 3 ：Let's substitute x = 3 into the polynomial and check if the result is zero.

Step 4 ：After substituting x = 3 into the polynomial, we get \(g(3)=3^{3}+2*3^{2}-9*3-18=0\).

Step 5 ：This confirms that 3 is indeed a zero of the polynomial.

Step 6 ：Final Answer: \(\boxed{0}\)