Answer :
Sure! Let's go through the synthetic division step-by-step.
In synthetic division, you divide a polynomial by a binomial of the form [tex]\(x - c\)[/tex]. Given that we have the setup [tex]\(2 \left\lvert\, \begin{array}{|cc|} \hline 1 & 5 \end{array}\right.\)[/tex]:
1. Understand the Setup:
- The number outside the division symbol (2) is the value of [tex]\(c\)[/tex] that comes from dividing by [tex]\(x - 2\)[/tex].
- The numbers inside the array (1 and 5) are the coefficients of the polynomial [tex]\(x + 5\)[/tex].
2. Bring Down the Leading Coefficient:
- Start by bringing down the leading coefficient, which is 1. This will be part of our quotient.
3. Multiply and Add:
- Multiply the number you brought down (1) by the number outside (2). This gives you [tex]\(2 \times 1 = 2\)[/tex].
- Add this result to the next coefficient inside the array, which is 5. So, [tex]\(5 + 2 = 7\)[/tex].
4. Form the Quotient:
- The first number you brought down is the coefficient of [tex]\(x\)[/tex].
- The result of the addition (7) is the constant term.
So, the quotient in polynomial form is [tex]\(x + 7\)[/tex].
Therefore, the correct answer is C. [tex]\(x + 7\)[/tex].
In synthetic division, you divide a polynomial by a binomial of the form [tex]\(x - c\)[/tex]. Given that we have the setup [tex]\(2 \left\lvert\, \begin{array}{|cc|} \hline 1 & 5 \end{array}\right.\)[/tex]:
1. Understand the Setup:
- The number outside the division symbol (2) is the value of [tex]\(c\)[/tex] that comes from dividing by [tex]\(x - 2\)[/tex].
- The numbers inside the array (1 and 5) are the coefficients of the polynomial [tex]\(x + 5\)[/tex].
2. Bring Down the Leading Coefficient:
- Start by bringing down the leading coefficient, which is 1. This will be part of our quotient.
3. Multiply and Add:
- Multiply the number you brought down (1) by the number outside (2). This gives you [tex]\(2 \times 1 = 2\)[/tex].
- Add this result to the next coefficient inside the array, which is 5. So, [tex]\(5 + 2 = 7\)[/tex].
4. Form the Quotient:
- The first number you brought down is the coefficient of [tex]\(x\)[/tex].
- The result of the addition (7) is the constant term.
So, the quotient in polynomial form is [tex]\(x + 7\)[/tex].
Therefore, the correct answer is C. [tex]\(x + 7\)[/tex].
