There are 12 actors auditioning for 5 different roles in a new play. how many different cast are possible

95,040 different cast are possible

Step-by-step explanation:

In this case the order in which the actors are selected for the 5 different roles is important. Therefore we use the permutations formula.

Where n is the number of items you can choose and choose r from them.

In this case and

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."