Scientists !!

Subjunctive mood - Discard B and C
D and E - the scientists believe , however, the structure of these two says it is widely believed.
IMO A

mv12 wrote:Scientists have recently received permission to research embryonic stem cells, derived from blastocysts or early-stage embryos, that they
believe to be capable of generating new cell growth and curing previously incurable ailments.
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(A)that they believe to be capable
(B) that they believe are capable
(C)that they believe will be capable
(D)believed as capable
(E) believed to be capable

Skeleton of the sentence:
Scientists have recently received permission to research embryonic stem cells that they believe to be capable of generating...

"Believe X to be Y"is the correct idiom.

We need "that" after stem cells. if we don't use that after stem cells, we get--in the options D and E-- "stem cells, believed...."
Now, know the rule.
NOUN+COMMA+VERB-ED, here Verb-ed modifies the NOUN before COMMA. In the options D and E, the intended meaning of the sentence will change.
Answer is thus A.