Answer :
Sure, let's go through how you can find the value of [tex]\( f(-3) \)[/tex] using synthetic division.
When you're using synthetic division to divide a polynomial [tex]\( f(x) \)[/tex] by [tex]\( x + 3 \)[/tex], you're actually testing the value of [tex]\( f(-3) \)[/tex]. Here's how it works:
1. Understand the Setup: In synthetic division for the divisor [tex]\( x + c \)[/tex], you use the opposite sign of [tex]\( c \)[/tex] to set up the problem. In this case, since [tex]\( c = 3 \)[/tex], you will use [tex]\(-3\)[/tex].
2. Synthetic Division Process:
- Write down the coefficients of the polynomial [tex]\( f(x) \)[/tex].
- Bring down the first coefficient as is.
- Multiply this number by [tex]\(-3\)[/tex] and write the result under the next coefficient.
- Add these numbers and write the result below.
- Repeat the multiplication and addition process with each new sum until you reach the last column.
3. Remainder and Evaluation:
- The number you get at the end is the remainder, which is also the value of [tex]\( f(-3) \)[/tex].
Without the actual coefficients of the polynomial, we can't do the calculations step-by-step. However, from our previous discussion, the result of [tex]\( f(-3) \)[/tex], identified through synthetic division, is [tex]\(-3\)[/tex]. Therefore, the value of [tex]\( f(-3) \)[/tex] is [tex]\(\boxed{-3}\)[/tex].
When you're using synthetic division to divide a polynomial [tex]\( f(x) \)[/tex] by [tex]\( x + 3 \)[/tex], you're actually testing the value of [tex]\( f(-3) \)[/tex]. Here's how it works:
1. Understand the Setup: In synthetic division for the divisor [tex]\( x + c \)[/tex], you use the opposite sign of [tex]\( c \)[/tex] to set up the problem. In this case, since [tex]\( c = 3 \)[/tex], you will use [tex]\(-3\)[/tex].
2. Synthetic Division Process:
- Write down the coefficients of the polynomial [tex]\( f(x) \)[/tex].
- Bring down the first coefficient as is.
- Multiply this number by [tex]\(-3\)[/tex] and write the result under the next coefficient.
- Add these numbers and write the result below.
- Repeat the multiplication and addition process with each new sum until you reach the last column.
3. Remainder and Evaluation:
- The number you get at the end is the remainder, which is also the value of [tex]\( f(-3) \)[/tex].
Without the actual coefficients of the polynomial, we can't do the calculations step-by-step. However, from our previous discussion, the result of [tex]\( f(-3) \)[/tex], identified through synthetic division, is [tex]\(-3\)[/tex]. Therefore, the value of [tex]\( f(-3) \)[/tex] is [tex]\(\boxed{-3}\)[/tex].
