Answer :
We are given the polynomial
[tex]$$
4x^2 + 6x - 1
$$[/tex]
and asked to perform synthetic division using [tex]$x=1$[/tex]. The synthetic division steps go as follows:
1. Write down the coefficients of the polynomial: [tex]$4$[/tex], [tex]$6$[/tex], and [tex]$-1$[/tex].
2. Bring the first coefficient down:
[tex]$$
b_0 = 4.
$$[/tex]
3. Multiply [tex]$b_0$[/tex] by [tex]$1$[/tex] (since [tex]$x=1$[/tex]):
[tex]$$
4 \times 1 = 4.
$$[/tex]
4. Add this result to the second coefficient:
[tex]$$
b_1 = 6 + 4 = 10.
$$[/tex]
5. Multiply [tex]$b_1$[/tex] by [tex]$1$[/tex]:
[tex]$$
10 \times 1 = 10.
$$[/tex]
6. Add this to the third coefficient to obtain the remainder:
[tex]$$
\text{Remainder} = -1 + 10 = 9.
$$[/tex]
Thus, the remainder is
[tex]$$
\boxed{9}.
$$[/tex]
[tex]$$
4x^2 + 6x - 1
$$[/tex]
and asked to perform synthetic division using [tex]$x=1$[/tex]. The synthetic division steps go as follows:
1. Write down the coefficients of the polynomial: [tex]$4$[/tex], [tex]$6$[/tex], and [tex]$-1$[/tex].
2. Bring the first coefficient down:
[tex]$$
b_0 = 4.
$$[/tex]
3. Multiply [tex]$b_0$[/tex] by [tex]$1$[/tex] (since [tex]$x=1$[/tex]):
[tex]$$
4 \times 1 = 4.
$$[/tex]
4. Add this result to the second coefficient:
[tex]$$
b_1 = 6 + 4 = 10.
$$[/tex]
5. Multiply [tex]$b_1$[/tex] by [tex]$1$[/tex]:
[tex]$$
10 \times 1 = 10.
$$[/tex]
6. Add this to the third coefficient to obtain the remainder:
[tex]$$
\text{Remainder} = -1 + 10 = 9.
$$[/tex]
Thus, the remainder is
[tex]$$
\boxed{9}.
$$[/tex]
