Answer :
To solve the synthetic division problem, we need to divide the polynomial [tex]\(4x + 6\)[/tex] by [tex]\(x - 2\)[/tex] and find the remainder. Let's go through the step-by-step process of synthetic division.
1. Set up the synthetic division:
- First, identify the coefficients of the polynomial, which are [tex]\(4\)[/tex] and [tex]\(6\)[/tex].
- The divisor is [tex]\(x - 2\)[/tex], so we use the root [tex]\(2\)[/tex] for synthetic division.
2. Perform synthetic division:
- Start by bringing down the first coefficient, which is [tex]\(4\)[/tex].
- Multiply the root [tex]\(2\)[/tex] by the number just brought down, which is [tex]\(4\)[/tex]. So, [tex]\(2 \times 4 = 8\)[/tex].
- Add this result to the next coefficient: [tex]\(6 + 8 = 14\)[/tex].
3. Interpret the results:
- The last number in the row is the remainder. In this case, the remainder is [tex]\(14\)[/tex].
Therefore, the remainder when [tex]\(4x + 6\)[/tex] is divided by [tex]\(x - 2\)[/tex] is [tex]\(14\)[/tex].
So, the correct choice from the given options is none of the above, as none of them match 14.
1. Set up the synthetic division:
- First, identify the coefficients of the polynomial, which are [tex]\(4\)[/tex] and [tex]\(6\)[/tex].
- The divisor is [tex]\(x - 2\)[/tex], so we use the root [tex]\(2\)[/tex] for synthetic division.
2. Perform synthetic division:
- Start by bringing down the first coefficient, which is [tex]\(4\)[/tex].
- Multiply the root [tex]\(2\)[/tex] by the number just brought down, which is [tex]\(4\)[/tex]. So, [tex]\(2 \times 4 = 8\)[/tex].
- Add this result to the next coefficient: [tex]\(6 + 8 = 14\)[/tex].
3. Interpret the results:
- The last number in the row is the remainder. In this case, the remainder is [tex]\(14\)[/tex].
Therefore, the remainder when [tex]\(4x + 6\)[/tex] is divided by [tex]\(x - 2\)[/tex] is [tex]\(14\)[/tex].
So, the correct choice from the given options is none of the above, as none of them match 14.
