To quickly do these kind of problems, we can use synthetic division. Let 4x+7=0 and solve for x. x=-7/4
-7/4 | 20 43 22
| -35 <---------------place product of 20 and -7/4 here
-----------------
20 <-----------bring down leading coefficient
-7/4 | 20 43 22
| -35 -14 <-------------place product of -7/4 and 8
-----------------
20 8 <--------------add 43 and -35 and place sum here
-7/4 | 20 43 22
| -35 -14
-----------------
20 8 8 <--------------add 22 and -14 and place sum here
Since the last number is 8, this is the remainder. We add the remainder to the quotient. Each number under the bar is a coefficient so the answer looks like
This technique allows us to quickly divide and get the same answer as polynomial long division. Hope this makes sense, ask about synthetic division if it doesn't make any sense.
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