Answer :
To solve the problem of dividing the polynomial [tex]\(2x + 7\)[/tex] by [tex]\(x + 1\)[/tex] using synthetic division, let's go through the steps below:
1. Identify the Dividend and Divisor:
The polynomial we are dividing is [tex]\(2x + 7\)[/tex], and the divisor is [tex]\(x + 1\)[/tex]. In synthetic division, we use the root of the divisor, which is [tex]\(-1\)[/tex], for calculations.
2. Set up the Synthetic Division Table:
Write the coefficients of the polynomial [tex]\(2x + 7\)[/tex] in a row. Since the polynomial is linear, the coefficients are [2, 7]. Below this row, we place the root of the divisor, which is [tex]\(-1\)[/tex].
3. Carry Down the Leading Coefficient:
To begin, carry down the leading coefficient, which is [tex]\(2\)[/tex], to the bottom row.
4. Multiply and Add:
- Multiply the number just brought down ([tex]\(2\)[/tex]) by the root of the divisor ([tex]\(-1\)[/tex]). This gives [tex]\(-2\)[/tex].
- Add this result to the next coefficient (7): [tex]\(7 + (-2) = 5\)[/tex].
5. Complete the Process:
There are no more coefficients in the original polynomial, so we finish the process here. At the end, we will have the numbers in the bottom row: [2, 5].
6. Interpret the Result:
The numbers in the bottom row represent the coefficients of the quotient polynomial. So, we have the quotient as [tex]\(2x + 5\)[/tex].
Therefore, the quotient of the division in polynomial form is [tex]\(2x + 5\)[/tex].
Thus, the correct choice is:
A. [tex]\(2x + 5\)[/tex]
1. Identify the Dividend and Divisor:
The polynomial we are dividing is [tex]\(2x + 7\)[/tex], and the divisor is [tex]\(x + 1\)[/tex]. In synthetic division, we use the root of the divisor, which is [tex]\(-1\)[/tex], for calculations.
2. Set up the Synthetic Division Table:
Write the coefficients of the polynomial [tex]\(2x + 7\)[/tex] in a row. Since the polynomial is linear, the coefficients are [2, 7]. Below this row, we place the root of the divisor, which is [tex]\(-1\)[/tex].
3. Carry Down the Leading Coefficient:
To begin, carry down the leading coefficient, which is [tex]\(2\)[/tex], to the bottom row.
4. Multiply and Add:
- Multiply the number just brought down ([tex]\(2\)[/tex]) by the root of the divisor ([tex]\(-1\)[/tex]). This gives [tex]\(-2\)[/tex].
- Add this result to the next coefficient (7): [tex]\(7 + (-2) = 5\)[/tex].
5. Complete the Process:
There are no more coefficients in the original polynomial, so we finish the process here. At the end, we will have the numbers in the bottom row: [2, 5].
6. Interpret the Result:
The numbers in the bottom row represent the coefficients of the quotient polynomial. So, we have the quotient as [tex]\(2x + 5\)[/tex].
Therefore, the quotient of the division in polynomial form is [tex]\(2x + 5\)[/tex].
Thus, the correct choice is:
A. [tex]\(2x + 5\)[/tex]
