Divide $p(x)$ by $g(x)$,where $p(x) = x + 3x^2 - 1$ and $g(x) = 1 + x$.

(N/A) We carry out the process of division by means of the following steps:
Step $1$: We write the dividend $x + 3x^2 - 1$ and the divisor $1 + x$ in the standard form,i.e.,after arranging the terms in the descending order of their degrees. So,the dividend is $3x^2 + x - 1$ and the divisor is $x + 1$.
Step $2$: We divide the first term of the dividend by the first term of the divisor,i.e.,we divide $3x^2$ by $x$,and get $3x$. This gives us the first term of the quotient.
Step $3$: We multiply the divisor by the first term of the quotient and subtract this product from the dividend,i.e.,we multiply $x + 1$ by $3x$ and subtract the product $3x^2 + 3x$ from the dividend $3x^2 + x - 1$. This gives us the remainder as $-2x - 1$.
Step $4$: We treat the remainder $-2x - 1$ as the new dividend. The divisor remains the same. We repeat Step $2$ to get the next term of the quotient,i.e.,we divide the first term $-2x$ of the new dividend by the first term $x$ of the divisor and obtain $-2$. Thus,$-2$ is the second term in the quotient.
Step $5$: We multiply the divisor by the second term of the quotient and subtract the product from the dividend. That is,we multiply $x + 1$ by $-2$ and subtract the product $-2x - 2$ from the dividend $-2x - 1$. This gives us $1$ as the remainder.
Step $6$: Thus,the quotient is $3x - 2$ and the remainder is $1$.
Verification: $3x^2 + x - 1 = (x + 1)(3x - 2) + 1$.