Answer :
Let's solve the synthetic division problem step by step!
We are dividing a polynomial by using synthetic division where [tex]\( c = 3 \)[/tex] (since the divisor would be in the form [tex]\( x - c \)[/tex], so [tex]\( c = 3 \)[/tex]).
Here are the steps for synthetic division:
1. Write the coefficients of the polynomial you're dividing. In this case, the polynomial is represented by the coefficients 1, 2, and -3.
2. Bring down the leading coefficient. Start by bringing down the first coefficient (1) directly below the line.
3. Multiply and add: Take this result (1) and multiply it by [tex]\( c \)[/tex] (which is 3), and add it to the next coefficient (2):
- [tex]\( 1 \times 3 = 3 \)[/tex]
- [tex]\( 2 + 3 = 5 \)[/tex]
4. Repeat the multiply and add step for the next coefficient (-3):
- [tex]\( 5 \times 3 = 15 \)[/tex]
- [tex]\(-3 + 15 = 12 \)[/tex]
5. The final result here, 12, is the remainder of the division.
So, the remainder when dividing the polynomial by [tex]\( x - 3 \)[/tex] using synthetic division is 12.
We are dividing a polynomial by using synthetic division where [tex]\( c = 3 \)[/tex] (since the divisor would be in the form [tex]\( x - c \)[/tex], so [tex]\( c = 3 \)[/tex]).
Here are the steps for synthetic division:
1. Write the coefficients of the polynomial you're dividing. In this case, the polynomial is represented by the coefficients 1, 2, and -3.
2. Bring down the leading coefficient. Start by bringing down the first coefficient (1) directly below the line.
3. Multiply and add: Take this result (1) and multiply it by [tex]\( c \)[/tex] (which is 3), and add it to the next coefficient (2):
- [tex]\( 1 \times 3 = 3 \)[/tex]
- [tex]\( 2 + 3 = 5 \)[/tex]
4. Repeat the multiply and add step for the next coefficient (-3):
- [tex]\( 5 \times 3 = 15 \)[/tex]
- [tex]\(-3 + 15 = 12 \)[/tex]
5. The final result here, 12, is the remainder of the division.
So, the remainder when dividing the polynomial by [tex]\( x - 3 \)[/tex] using synthetic division is 12.
