Answer :
Given the polynomial
[tex]$$4x^2 + 6x - 1$$[/tex]
and the divisor
[tex]$$x - 1,$$[/tex]
we perform synthetic division using the root [tex]$1$[/tex] (since [tex]$x-1=0$[/tex] when [tex]$x=1$[/tex]).
1. Write down the coefficients of the polynomial: [tex]$4$[/tex], [tex]$6$[/tex], and [tex]$-1$[/tex].
2. Bring down the first coefficient:
[tex]$$\text{First coefficient} = 4.$$[/tex]
3. Multiply this result by [tex]$1$[/tex] (the root) and add it to the next coefficient:
[tex]$$ 4 \times 1 = 4,$$[/tex]
[tex]$$ 6 + 4 = 10. $$[/tex]
4. Multiply the new result by [tex]$1$[/tex]:
[tex]$$ 10 \times 1 = 10,$$[/tex]
and add it to the constant term:
[tex]$$ -1 + 10 = 9. $$[/tex]
Thus, the remainder of the division is
[tex]$$\boxed{9}.$$[/tex]
[tex]$$4x^2 + 6x - 1$$[/tex]
and the divisor
[tex]$$x - 1,$$[/tex]
we perform synthetic division using the root [tex]$1$[/tex] (since [tex]$x-1=0$[/tex] when [tex]$x=1$[/tex]).
1. Write down the coefficients of the polynomial: [tex]$4$[/tex], [tex]$6$[/tex], and [tex]$-1$[/tex].
2. Bring down the first coefficient:
[tex]$$\text{First coefficient} = 4.$$[/tex]
3. Multiply this result by [tex]$1$[/tex] (the root) and add it to the next coefficient:
[tex]$$ 4 \times 1 = 4,$$[/tex]
[tex]$$ 6 + 4 = 10. $$[/tex]
4. Multiply the new result by [tex]$1$[/tex]:
[tex]$$ 10 \times 1 = 10,$$[/tex]
and add it to the constant term:
[tex]$$ -1 + 10 = 9. $$[/tex]
Thus, the remainder of the division is
[tex]$$\boxed{9}.$$[/tex]
