is divisible by . Find q.
Two obvious paths to answering the question:
(1) long division, or synthetic division; remainder must be zero
(2) divisible by 3x-4 means x=4/3 is a root; evaluate p(4/3) and solve the resulting equation for q
(1) If the polynomial is divisible by 3x-4, then it is divisible by x-(4/3). Use synthetic division with 4/3.
4/3 | -6 -7 q -12
| -8 -20 (4/3)(q-20)
+--------------------------
-6 -15 q-20 0
The remainder has to be 0:
ANSWER: q = 29
(2) Set p(4/3)=0 and solve for q.
ANSWER: q = 29