Sec $11\mathrm{.}3$: #$3$ Suppose an algorithm requires cn$3$ operations when performed with an input of size n $($where c is a constant$).$ a$.$How many operations will be required when the input size is increased from m to $2$m $($where m is a positive integer$)?$ b$.$By what factor will the number of operations increase when the input size is doubled? c$.$ By what factor will the number of operations increase when the input size is increased by a factor of ten?