G(x) = px² + qx + x² + 5 - 18
= (p + 1)x² + qx - 13

Then, using synthetic division, we have:

-2 | (p + 1) . . . . + q . . . . . . . . . . . .- 13
. . . . . . . . . - 2(p + 1). . . . . . -2[-2(p + 1) + q]
. . .(p + 1) . - 2(p + 1) + q . . . -2[-2(p + 1) + q] - 13

So the quotient is:

(p + 1)x - 2(p + 1) + q
= px + x - 2p - 2 + q

The remainder is:

-2[-2(p + 1) + q] - 13
= 4(p + 1) - 2q - 13
= 4p + 4 - 2q - 13
= 4p - 2q - 9

I hope this helps!

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