For this problem we need to remember our difference of cubes which says a ^3 -, b ^3 factors into A -, B * a ^2 plus AB plus b ^2. So in this problem, when I see that s ^3 - 512 and I see the s ^2 - 64, this top is going to turn into s - 8 * s ^2 + 8 S plus 64. The bottom is the difference of two squares, so that's s -, 8 * s + 8. So the S minus eights are going to cancel, and we get an s ^2 + 8 S plus 64, all divided by s + 8, knowing that S can never equal 8. So now, because we're wanting to figure out the continuous extension, what we're really being asked to do is to figure out what's the limit as S approaches 8 of that simplified equation. So s ^2 + 8, S plus 64 / s + 8. So when I put in eight, not Infinity, we're going to get 8 ^2. That looks pretty awful. 8 ^2 + 8 * 8 plus 64 all over 8 + 8, so 64 + 64 + 64 / 16. So 360 fours is going to give us 192. If we divide that by 16, we're going to get 12. So the limit as S approaches 8 is 12, and we knew S couldn't be defined at 8:00. So we want F of eight to equal 12 to have a continuous extension. We have a new definition of a function, so F is usually used as a capital. With a continuous extension, F of X is going to equal little F of X everywhere when X is not equal to 8, and it's going to equal 12 when X does equal 8.