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:

-4x³ - 1x³
(-4 - 1)x³
-5x³

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:

\( \frac{4!}{6!} \)
\( \frac{4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5} \)
\( \frac{1}{30} \)

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{16}{9}} \)
\( \frac{\sqrt{16}}{\sqrt{9}} \)
\( \frac{\sqrt{4^2}}{\sqrt{3^2}} \)
\( \frac{4}{3} \)
1\(\frac{1}{3}\)

The equation for this sequence is:

a_n = a_n-1 + 9

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 9
a₆ = 37 + 9
a₆ = 46

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

vans = \( \frac{65}{14} \) = 4\(\frac{9}{14}\)

So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.