How do you use synthetic division to divide `y^2 + 25` by `y+5`?

`y^2+25 = y^2+0y+25` is represented by the sequence `1`, `0`, `25`.

`y+5` is represented by the sequence `1`, `5`.

Write out like long division of integers and proceed similarly:

Write `1`, `0`, `25` under the bar as the dividend and `1`, `5` to the left as the divisor.

Identify `1` as the first term of the quotient - writing it above the bar - choosing it to cause the leading terms to match when the divisor is multiplied by it.

Write out `1 xx (1, 5)` under the dividend and subtract it to get the first term `-5` of a remainder.

Bring down the next term `25` of the dividend alongside it.

Identify `-5` as the second term of the quotient - writing above the bar - choosing it to cause the leading terms to match when the divisor is multiplied by it.

Write out `-5 xx (1, 5)` under the remainder and subtract it to get the remainder `50`.

We stop with this remainder since there are not enough terms remaining to make a sequence with enough terms to be divisible by the divisor.

So we have found:

`(y^2 + 25)/(y+5) = (y-5) + 50/(y+5)`

or if you prefer:

`y^2 + 25 = (y+5)(y-5) + 50`