(b) Find the remainder and quotient if the polynomial $$ f(x)=x^{3}+3 x^{2}-15 x-10 $$ is divided by $$ x-3 $$

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1. Write down the coefficients of $$ f(x)=x^{3}+3x^{2}-15x-10 $$:  
   $$
   1, \quad 3, \quad -15, \quad -10
   $$

2. Since we are dividing by $$ x - 3 $$, use synthetic division with $$ c=3 $$.

3. Set up the synthetic division:
   
   - Bring down the first coefficient: $$ 1 $$.
   - Multiply $$ 1 $$ by $$ 3 $$ and write the result under the next coefficient: $$ 1 \times 3 = 3 $$.
   - Add: $$ 3 + 3 = 6 $$.
   - Multiply $$ 6 $$ by $$ 3 $$: $$ 6 \times 3 = 18 $$.
   - Add: $$ -15 + 18 = 3 $$.
   - Multiply $$ 3 $$ by $$ 3 $$: $$ 3 \times 3 = 9 $$.
   - Add: $$ -10 + 9 = -1 $$.

4. The synthetic division yields the coefficients $$ 1 $$, $$ 6 $$, and $$ 3 $$ for the quotient polynomial, with a remainder of $$ -1 $$.

5. Therefore, the quotient when $$ f(x) $$ is divided by $$ x-3 $$ is:
   $$
   x^2 + 6x + 3
   $$
   and the remainder is:
   $$
   -1.
   $$
The quotient is $$ x^2 + 6x + 3 $$ and the remainder is $$ -1 $$.

(b) Find the remainder and quotient if the polynomial is divided by

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