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]

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Rewritten by : Barada