When \(x^3 +30x -c\)is divided by \(x-5\) the remainder is\(5\). 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,
\((5)^3+30(5)-c=5\\ 125+150-c=5\\ 275-c=5\\ c=270\)
Same answer as guest :)
I like tt's method better....I didn't think of that !
