What happens to the divisor after obtaining the first term of the quotient in polynomial long division?

In polynomial long division, after obtaining the first term of the quotient, the divisor is indeed multiplied by that first term. This process is a fundamental step in long division, analogous to the way numbers are handled in numerical long division.

To detail this process, you initially divide the leading term of the dividend by the leading term of the divisor. This gives you the first term of the quotient. Next, this term is multiplied by the entire divisor, resulting in a polynomial that is then subtracted from the original dividend. This subtraction allows you to find the remainder of the polynomial division and continue the process with the new polynomial.

This step is critical because it sets up the next iteration of the division to find further terms in the quotient. It’s important to understand that multiplying the first term of the quotient by the divisor helps in progressively breaking down the polynomial until the remainder is of a lower degree than the divisor, which completes the division process.

Thus, the correct answer reflects the essential mechanics of polynomial long division.