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Answer :
To solve this synthetic division problem, you are dividing the polynomial [tex]\( x + 5 \)[/tex] by [tex]\( 2 \)[/tex]. Let's go through the steps:
1. Identify the Dividend and Divisor:
- The polynomial (dividend) is [tex]\( x + 5 \)[/tex].
- The divisor is indicated as [tex]\( 2 \)[/tex]. In synthetic division, we typically use a divisor in the form [tex]\( x - c\)[/tex]. Here, [tex]\( c \)[/tex] is [tex]\( -2 \)[/tex] because it would correspond to a divisor of [tex]\( (x - (-2)) = (x + 2) \)[/tex].
2. Synthetic Division Setup:
- We only need the coefficients of the polynomial [tex]\( x + 5 \)[/tex], which are [tex]\( 1 \)[/tex] (for [tex]\( x \)[/tex]) and [tex]\( 5 \)[/tex] (for the constant).
- You'll be dividing by [tex]\( 2 \)[/tex].
3. Perform Synthetic Division:
- Start with the leading coefficient [tex]\( 1 \)[/tex].
- Multiply this by the divisor, [tex]\( 2 \)[/tex], and add the result to the next coefficient, [tex]\( 5 \)[/tex]:
- [tex]\( 1 \times 2 = 2 \)[/tex]
- [tex]\( 5 + 2 = 7 \)[/tex]
4. Write the Quotient:
- The synthetic division result tells us the quotient in polynomial form. The quotient is [tex]\( x + 7 \)[/tex].
So, the quotient in polynomial form is [tex]\( x + 7 \)[/tex], which corresponds to option A.
1. Identify the Dividend and Divisor:
- The polynomial (dividend) is [tex]\( x + 5 \)[/tex].
- The divisor is indicated as [tex]\( 2 \)[/tex]. In synthetic division, we typically use a divisor in the form [tex]\( x - c\)[/tex]. Here, [tex]\( c \)[/tex] is [tex]\( -2 \)[/tex] because it would correspond to a divisor of [tex]\( (x - (-2)) = (x + 2) \)[/tex].
2. Synthetic Division Setup:
- We only need the coefficients of the polynomial [tex]\( x + 5 \)[/tex], which are [tex]\( 1 \)[/tex] (for [tex]\( x \)[/tex]) and [tex]\( 5 \)[/tex] (for the constant).
- You'll be dividing by [tex]\( 2 \)[/tex].
3. Perform Synthetic Division:
- Start with the leading coefficient [tex]\( 1 \)[/tex].
- Multiply this by the divisor, [tex]\( 2 \)[/tex], and add the result to the next coefficient, [tex]\( 5 \)[/tex]:
- [tex]\( 1 \times 2 = 2 \)[/tex]
- [tex]\( 5 + 2 = 7 \)[/tex]
4. Write the Quotient:
- The synthetic division result tells us the quotient in polynomial form. The quotient is [tex]\( x + 7 \)[/tex].
So, the quotient in polynomial form is [tex]\( x + 7 \)[/tex], which corresponds to option A.
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