A judgment will be seen as synthetic when it is a fact and the predicate concept is not contained in the subject concept. An example would be, all creatures with kidneys have hearts. The example does not contain the predicate concept stating nothing new about the subject, hence why it is considered a synthetic judgment. Unlike analytic judgments, synthetic judgments cannot be proven to be true or false, which is a problem faced when dealing with them. .
Kant's theories go further than just analytic and synthetic, he explains a second theory known as a priori and a posterior, which allows us to identify whether, a judgment is true or false with given information. A judgment can be identified as a priori when it is known from experience; for example all triangles have three sides. We do not need to research on the fact that all triangles have three sides because it is world known. A judgment is known as a posterior when it is known from knowledge that we can only have after we experience it or observe it to gain knowledge. For example smoking causes cancer, research had to be done in order for people to start to realize that smoking actually causes cancer. .
From these distinctions Kant was able to come up with three possible types of judgments. The first is when a judgment is analytically true we know this as a priori because we do not need experience to tell us what is contained in our concepts; and for this reason there are no analytic a posteriori judgments (Kant 235). The second is when a judgment is seen as a posteriori or from experience then this is seen as synthetic. We see this as it is because the subject and the predicate are "synthesized " (Kant 236), for example we learn from experience that the grass is green and not red. The final kind of judgment is synthetic a priori, Kant explains this, as something that tells us something knew about the subject and yet it is partly known from experience on the basis of reasoning.