Answer :
Sure! Let's tackle the synthetic division problem step by step.
We are dividing the polynomial "2x + 7" by "x + 1" using synthetic division. Here's how you can do it:
1. Set up the problem for synthetic division:
- Write down the coefficients of the polynomial you want to divide. In this case, it's [tex]\(2x + 7\)[/tex], so the coefficients are 2 and 7.
- Write the root of the divisor [tex]\(x + 1\)[/tex]. To find the root, set [tex]\(x + 1 = 0\)[/tex], which gives [tex]\(x = -1\)[/tex].
2. Perform synthetic division:
- Start by writing the leading coefficient (2) of the polynomial on the left. This will be the starting point of our calculations.
- Multiply this number by the root [tex]\(-1\)[/tex] and write the result under the next coefficient (7).
- Add the result to the next coefficient: [tex]\(7 + (2 \times -1) = 7 - 2 = 5\)[/tex].
3. Result:
- The numbers you just calculated represent the coefficients of the quotient polynomial.
- Therefore, the quotient is [tex]\(2x + 5\)[/tex].
So, the quotient in polynomial form from dividing [tex]\(2x + 7\)[/tex] by [tex]\(x + 1\)[/tex] is [tex]\(2x + 5\)[/tex].
Thus, the correct choice is C. [tex]\(2x + 5\)[/tex].
We are dividing the polynomial "2x + 7" by "x + 1" using synthetic division. Here's how you can do it:
1. Set up the problem for synthetic division:
- Write down the coefficients of the polynomial you want to divide. In this case, it's [tex]\(2x + 7\)[/tex], so the coefficients are 2 and 7.
- Write the root of the divisor [tex]\(x + 1\)[/tex]. To find the root, set [tex]\(x + 1 = 0\)[/tex], which gives [tex]\(x = -1\)[/tex].
2. Perform synthetic division:
- Start by writing the leading coefficient (2) of the polynomial on the left. This will be the starting point of our calculations.
- Multiply this number by the root [tex]\(-1\)[/tex] and write the result under the next coefficient (7).
- Add the result to the next coefficient: [tex]\(7 + (2 \times -1) = 7 - 2 = 5\)[/tex].
3. Result:
- The numbers you just calculated represent the coefficients of the quotient polynomial.
- Therefore, the quotient is [tex]\(2x + 5\)[/tex].
So, the quotient in polynomial form from dividing [tex]\(2x + 7\)[/tex] by [tex]\(x + 1\)[/tex] is [tex]\(2x + 5\)[/tex].
Thus, the correct choice is C. [tex]\(2x + 5\)[/tex].
