Answer:
P(3) = 0, so a=3 is a zero of the polynomial
Explanation:
Set up the synthetic division as seen in the picture:
1. Since a=3, the 3 is in the box at the left
2. Make sure you have EVERY term in the polynomial (ie, if the highest degree is 3 there must be 4 terms with successively decreasing exponents). P(x) has all of its terms, so we're good.
3. Write the coefficients and constant of the polynomial in order.
Synthetic Division process:
1. Bring down the first number
2. Multiply that number by the one in the box (3)
3. Place that product just below the second number
4. Add those two numbers together
5. Repeat steps 2-4 with all remaining numbers
The last sum is the remainder. If it is zero, then the number in the box is a zero/solution to the polynomial.