Answer :
Sure! Let's go through the synthetic division process step-by-step to find the remainder for this problem:
We're dividing the polynomial [tex]\(4x + 6\)[/tex] by [tex]\(x + 3\)[/tex].
1. Identify the coefficients of the polynomial:
- The polynomial is [tex]\(4x + 6\)[/tex].
- The coefficients are 4 and 6.
2. Identify the divisor:
- The divisor is [tex]\(x + 3\)[/tex].
- We use the opposite of the number in the divisor for synthetic division, which is [tex]\(-3\)[/tex].
3. Setup for synthetic division:
- Write the coefficients in a row: 4 and 6.
- Place the number [tex]\(-3\)[/tex] to the left.
4. Perform the calculations:
- Bring down the first coefficient 4 directly.
- Multiply this 4 by [tex]\(-3\)[/tex] (the divisor) to get [tex]\(-12\)[/tex].
- Add [tex]\(-12\)[/tex] to the next coefficient 6.
- [tex]\(6 + (-12) = -6\)[/tex].
5. The result:
- The final value, [tex]\(-6\)[/tex], is the remainder of the synthetic division process.
Therefore, the remainder when dividing [tex]\(4x + 6\)[/tex] by [tex]\(x + 3\)[/tex] is [tex]\(-6\)[/tex].
We're dividing the polynomial [tex]\(4x + 6\)[/tex] by [tex]\(x + 3\)[/tex].
1. Identify the coefficients of the polynomial:
- The polynomial is [tex]\(4x + 6\)[/tex].
- The coefficients are 4 and 6.
2. Identify the divisor:
- The divisor is [tex]\(x + 3\)[/tex].
- We use the opposite of the number in the divisor for synthetic division, which is [tex]\(-3\)[/tex].
3. Setup for synthetic division:
- Write the coefficients in a row: 4 and 6.
- Place the number [tex]\(-3\)[/tex] to the left.
4. Perform the calculations:
- Bring down the first coefficient 4 directly.
- Multiply this 4 by [tex]\(-3\)[/tex] (the divisor) to get [tex]\(-12\)[/tex].
- Add [tex]\(-12\)[/tex] to the next coefficient 6.
- [tex]\(6 + (-12) = -6\)[/tex].
5. The result:
- The final value, [tex]\(-6\)[/tex], is the remainder of the synthetic division process.
Therefore, the remainder when dividing [tex]\(4x + 6\)[/tex] by [tex]\(x + 3\)[/tex] is [tex]\(-6\)[/tex].
