For the first blank, we're looking for a synonym of "controversial" or polemical. The second blank is a little trickier. We need something that reflects the power of the education lobby, and that is not normally questioned. "Hegemony" means authority, power, dominance, etc., and is the best fit here. 

The peas are viewed "with disgust" and described as "despised." Harold hates them, or finds them "odious." For the second blank, we need something meaning not complaisant (obedient) and "not giving in any time soon." "Intransigence" means stubbornness or refusing to compromise, so this is a good fit.

The word "normally" and the comma are clues that there is a change, and the blanks will likely be opposites. So the correct answer is "brusque"—abrupt or curt in manner or speech—and "ingratiated"—to please someone or seek favor.

The doctoral student has published successfully, so she must be intelligent or insightful enough to do this, the definition of "perspicacious." "Substantiate," meaning to provide evidence, is the only answer that makes sense in the second sentence.

The smell of the cheese is different from the "perfume of various oils and herbs." This means it is pungent or sharp, the definition of "acrid." It is being hidden or covered, the definition of "obscured," by the herbs and oils.

The girl's story "moved many to give," and this points to both answers, as the story is strong enought to get funds for the organization. "Poignant," meaning deeply moving, and "solicit," meaning to ask or seek out, combine for the correct answer.

Amalgamate—to mix or merge as to make a combination.

Amenable—agreeable.

The group leader wanted to combine the individual contributions so that all of the group members were happy with the outcome.

Our hint for the second blank is "divisions", so we're looking for words that match that. "Polarize" is our best choice, which means "to divide into two groups." But we still have to check the other word—"exigent" means "pressing," so it works as well.

For the first blank, we need an adjective that means something like secretive. Either "enigmatic" (difficult to interpret or understand; mysterious) or "taciturn" (reserved or uncommunicative in speech; saying little) could work.

For the second blank, we need a verb that means to reveal only a small part of, since the master thief kept most of the details of his plan to himself. In choosing between "precipitate" (cause something (usually something bad) to happen suddenly, unexpectedly, or prematurely) and "adumbrate" (to suggest, disclose, or outline partially), "adumbrate" is the better choice, so the answer is "enigmatic . . . adumbrate."

For the first blank, we're looking for a word with a positive connotation, since the plumber did a good job in quickly stopping the leak. Knowing this, we can eliminate the answer choices that begin with "indifferent," "hapless," and "officious," all words with neutral or negative meanings, leaving us with "laudable" and "commendable," two words with positive connotations. For the second blank, we're looking for a word that means stopping or blocking. Since "exacerbating" means making worse and "occluding" means obstructing an opening, the correct answer is "laudable . . . occluding."