what is the remainder when (3x^3 - 2x^2 + 4x - 3) is divided by (x^2 + 3x + 3)?\n30\n3x - 11\n28x - 36\n28x…

Explanation:

Step1: Set up polynomial long - division

We divide the polynomial $3x^{3}-2x^{2}+4x - 3$ by $x^{2}+3x + 3$. The first term of the quotient is obtained by dividing the leading term of the dividend $3x^{3}$ by the leading term of the divisor $x^{2}$. So, $\frac{3x^{3}}{x^{2}}=3x$.

Step2: Multiply and subtract

Multiply $x^{2}+3x + 3$ by $3x$: $3x(x^{2}+3x + 3)=3x^{3}+9x^{2}+9x$. Subtract this from the dividend: $(3x^{3}-2x^{2}+4x - 3)-(3x^{3}+9x^{2}+9x)=3x^{3}-2x^{2}+4x - 3 - 3x^{3}-9x^{2}-9x=-11x^{2}-5x - 3$.

Step3: Find the next term of the quotient

Divide the leading term of the new dividend $-11x^{2}$ by the leading term of the divisor $x^{2}$, $\frac{-11x^{2}}{x^{2}}=-11$.

Step4: Multiply and subtract again

Multiply $x^{2}+3x + 3$ by $-11$: $-11(x^{2}+3x + 3)=-11x^{2}-33x - 33$. Subtract this from $-11x^{2}-5x - 3$: $(-11x^{2}-5x - 3)-(-11x^{2}-33x - 33)=-11x^{2}-5x - 3 + 11x^{2}+33x + 33 = 28x+30$.

Answer:

D. $28x + 30$