When x3+30x−cis divided by x−5 the remainder is5. What is c?
Long division
______x2__+5x_ +55_______
x-5 | x^3 + 30x -c
x^3 - 5x^2
5x^2 + 30x -c
5x^2 - 25x
55x -c
55x - 275
-c + 275
-c + 275 = 5 (the remainder)
-c = - 270
c = 270 (if I made no mistakes....check it!)
Faster solution:
The remainder theorem tells us that the remainder is the value of x^3+30x-c when x = 5.
Therefore,
(5)3+30(5)−c=5125+150−c=5275−c=5c=270
Same answer as guest :)
I like tt's method better....I didn't think of that !
