Polarity, Monster Levels and Skills
There are three types of monsters that can be synthesized together. There are plus monsters (+), minus monsters(-), and neutral monsters and that symbol is shown with a (+-). Only monsters at level 10 can be synthesized. Also monsters can only be synthesized if they have opposite polarities, so (+) monsters combine with (-) monsters and (+-) monsters can be combined with (+) and (-) monsters, but not with other (+-) monsters. The result monster can also receive the 'parent' monsters skill sets and receive new ones. Each skill set keeps half of the allocated skill points.
Some weapons can alter the final monster's polarity or form. These are the Minus Sceptre, the Plus Sceptre and the Phoenix Sceptre. As their names suggest, the Minus and Plus Sceptres make a monster a (+) or a (-) monster. When a monster holds a Phoenix Sceptre, it retains it's form through synthesis.
Special Synthesis and Quad Synthesis
Some specific synthesis recipes involve combining two of the same monster together or a generic monster with a specific monster family. These recipes usually create a more powerful monster that is usually a rank A through X. Some examples would be the combination of a great dragon and a metal dragon to create a mechan-o'-wyrm, the combination of a great dragon with a demon-at-arms to create a Dragonlord or the combination of a jumping jackal and a heligator to create a riptide. Another form of special synthesis would be quad synthesis. This form of synthesis shows involves the special combination of the 'grandparent' monster to create the two 'parent monsters.
There are some specific recipes used to create powerful monsters from previous games. An example would be the synthesis of a Great Dragon and a Demon-at-arms to create the main antagonist of Dragon Quest, Dragonlord. this is a powerful rank S monster.
This synthesis technique involves lots of saving, so an easy and common example of this would be the synthesis of a mumboh-jumboe. If you wish to create this Rank S monster, save constantly and pay close attention. In order to do this right, you must get 4 jums. To get all the requested skills for the final monster, you can synthesize these. Then synthesize 3 of the jums to create a mum (jum x material family), a boh (jum x beast family), and a boe (jum x nature family). Once you have a mum, a boh, a jum and a boe, save to guarantee the monster can be made. The combination of these 4 monsters doesn't matter, as the recipe suggests, but from the pairs of these monsters you can form a mum or a living statue. Warning: save before combining to ensure both monsters have the opposite polarity. After creating a mum or living statue of opposite polarities, train these monsters as much as you want, but make sure you keep these two monsters from synthesizing with other monsters. After the desired skills are received, you can synthesize these together and you will have a rank S mumboh-jumboe.