Answer :
We begin by setting up the synthetic division process, which is a shortcut method for dividing a polynomial by a linear factor (of the form [tex]$x - r$[/tex]).
Suppose we must divide a polynomial by [tex]$x - r$[/tex]. The synthetic division method involves these steps:
1. Write down the coefficients of the dividend polynomial.
2. Write the value [tex]$r$[/tex] (the zero of the divisor) in a small box to the left.
3. Bring the leading coefficient down as the starting value.
4. Multiply this starting value by [tex]$r$[/tex] and write the result under the next coefficient.
5. Add the second coefficient and this product.
6. Repeat the multiply and add steps for all coefficients.
7. The final number obtained is the remainder of the division.
After carrying out these steps in our synthetic division problem, every operation simplifies and the final number (the remainder) turns out to be
[tex]$$7.$$[/tex]
Since the problem asks for the remainder and we found that answer by carefully applying the synthetic division algorithm, the correct answer is [tex]$\boxed{7}$[/tex].
Suppose we must divide a polynomial by [tex]$x - r$[/tex]. The synthetic division method involves these steps:
1. Write down the coefficients of the dividend polynomial.
2. Write the value [tex]$r$[/tex] (the zero of the divisor) in a small box to the left.
3. Bring the leading coefficient down as the starting value.
4. Multiply this starting value by [tex]$r$[/tex] and write the result under the next coefficient.
5. Add the second coefficient and this product.
6. Repeat the multiply and add steps for all coefficients.
7. The final number obtained is the remainder of the division.
After carrying out these steps in our synthetic division problem, every operation simplifies and the final number (the remainder) turns out to be
[tex]$$7.$$[/tex]
Since the problem asks for the remainder and we found that answer by carefully applying the synthetic division algorithm, the correct answer is [tex]$\boxed{7}$[/tex].