Part 1 of 2 (a) Divide $$ \left(3 x^{3}-6 x^{2}+10 x-3\right)+(x-3) $$ and identify the divisor, quotient, and remainder, Divisor: Quotient: $$ \square $$

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We begin by combining the two expressions:

$$
\left(3x^3 - 6x^2 + 10x - 3\right) + (x - 3) = 3x^3 - 6x^2 + 11x - 6.
$$

We now interpret the problem as dividing the polynomial

$$
3x^3 - 6x^2 + 11x - 6
$$

by the divisor

$$
x - 3.
$$

We set up synthetic division using the zero of $$x - 3$$, which is $$3$$.

The coefficients of the dividend are: $$3,\; -6,\; 11,\; -6$$.

1. Bring down the first coefficient: $$3$$.
2. Multiply $$3$$ by $$3$$ to get $$9$$; add to $$-6$$ to obtain $$3$$.
3. Multiply $$3$$ by $$3$$ to get $$9$$; add to $$11$$ to obtain $$20$$.
4. Multiply $$20$$ by $$3$$ to get $$60$$; add to $$-6$$ to obtain $$54$$.

Thus, the synthetic division produces the quotient coefficients $$3,\; 3,\; 20$$ and the remainder $$54$$. In other words, we have:

$$
\frac{3x^3 - 6x^2 + 11x - 6}{x - 3} = 3x^2 + 3x + 20 \quad \text{with remainder } 54.
$$

Divisor: $$x - 3$$  
Quotient: $$3x^2 + 3x + 20$$  
Remainder: $$54$$
Divisor: $$x - 3$$ Quotient: $$3x^2 + 3x + 20$$ Remainder: $$54$$

Part 1 of 2
(a) Divide and identify the divisor, quotient, and remainder,
Divisor:
Quotient:

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Part 1 of 2 (a) Divide and identify the divisor, quotient, and remainder, Divisor: Quotient: