If f(x)=x^3+9x^2+2x-48 and f(-3)=0 . th algebraically.

To find the other zeros of the polynomial \( f(x) = x^3 + 9x^2 + 2x - 48 \) given that \( f(-3) = 0 \), we can use synthetic division to factor out \( (x + 3) \) from the polynomial.### Step 1: Synthetic DivisionWe will perform synthetic division using .1. Write down the coefficients of \( f(x) \): 2. Set up the synthetic division: Here's the step-by-step process:- Bring down the leading coefficient (1).- Multiply -3 by 1 and write it under the next coefficient: .- Add the second coefficient (9) and -3: \( 9 + (-3) = 6 \).- Multiply -3 by 6 and write it under the next coefficient: .- Add the third coefficient (2) and -18: \( 2 + (-18) = -16 \).- Multiply -3 by -16 and write it under the next coefficient: .- Add the fourth coefficient (-48) and 48: .The bottom row gives us the coefficients of the quotient polynomial: ### Step 2: Solve the Quotient PolynomialNow we need to find the zeros of the quadratic polynomial .We can use the quadratic formula , where , , and . This gives us two solutions: ### Step 3: List All ZerosThe zeros of the polynomial \( f(x) = x^3 + 9x^2 + 2x - 48 \) are: