Now the woman was a Greek, a Syrophoenician by race. And she besought him that he would cast forth the demon out of her daughter.

Now she was a Greek woman of Syrophoenician origin, and she kept asking Jesus to drive the demon out of her daughter.

and the woman was a Greek, a Syro-Phenician by nation--and was asking him, that the demon he may cast forth out of her daughter.

(and the woman was a Greek, Syrophenician by race), and asked him that he would cast the demon out of her daughter.