A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

6x³ - 9x³
(6 - 9)x³
-3x³

To simplify a radical, factor out the perfect squares:

\( \sqrt{20} \)
\( \sqrt{4 \times 5} \)
\( \sqrt{2^2 \times 5} \)
2\( \sqrt{5} \)

First, solve for \( \left|c - 3\right| \):

\( \left|c - 3\right| \) + 6 = -4
\( \left|c - 3\right| \) = -4 - 6
\( \left|c - 3\right| \) = -10

The value inside the absolute value brackets can be either positive or negative so (c - 3) must equal - 10 or --10 for \( \left|c - 3\right| \) to equal -10:

So, c = 13 or c = -7.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{68}{12} \) = 5\(\frac{2}{3}\)

So, it will take 5 full vans and one partially full van to transport the entire team making a total of 6 vans.