what is the quotient of $(x^{3}+3x^{2}+5x + 3)div(x + 1)$?\n$x^{2}+4x + 9$\n$x^{2}+2x$\n$x^{2}+2x +…

Explanation:

Step1: Use polynomial long - division

Divide the first term of the dividend $x^{3}+3x^{2}+5x + 3$ (which is $x^{3}$) by the first term of the divisor $x + 1$ (which is $x$). The result is $x^{2}$. Multiply $x + 1$ by $x^{2}$ to get $x^{3}+x^{2}$, and subtract it from the dividend: $(x^{3}+3x^{2}+5x + 3)-(x^{3}+x^{2})=2x^{2}+5x + 3$.

Step2: Repeat the process

Divide the first term of the new dividend $2x^{2}+5x + 3$ (which is $2x^{2}$) by the first term of the divisor $x$ (from $x + 1$). The result is $2x$. Multiply $x + 1$ by $2x$ to get $2x^{2}+2x$, and subtract it from the new dividend: $(2x^{2}+5x + 3)-(2x^{2}+2x)=3x + 3$.

Step3: Do it one more time

Divide the first term of the new dividend $3x + 3$ (which is $3x$) by the first term of the divisor $x$ (from $x + 1$). The result is $3$. Multiply $x + 1$ by $3$ to get $3x+3$, and subtract it from the new dividend: $(3x + 3)-(3x + 3)=0$.

Answer:

C. $x^{2}+2x + 3$