Algebra: Multiplying and adding polynomials

In drag racing, both vehicles begin at a dead stop, and then accelerate through 1/4 mi. Let us say, for the sake of discussion, that our two vehicles are not quite matched in power. That is, vehicle A can accelerate from 0 mph to 60 mph in 5 secs. Whereas the vehicle B can accelerate from 0 mph to 60 mph in 4 secs.

DQ 1: So, the question arises, how would you calculate the position of each vehicle after t secs? For instance, t = 5 or t = 6. Note: remember to convert from miles per hour to miles per second.
DQ 2: How would you determine the distance between the two vehicles after t secs?
DQ 3: How would you determine the time, t, for the fastest vehicle to traverse 1/4 mi.?
DQ 4: In the Indianapolis 500, the vehicles do not begin at a dead stop. In fact, a pace car sets the initial velocity; let us say it is 80 mph. If the lead vehicle can accelerate 0 to 100 mph in 5 secs, what would be the position of the lead vehicle from the starting point after t secs, for instance, t = 5 or t = 6?

Please see the attached file for the fully formatted problems.

Section 4.1 - The Power of a Quotient Rule
Simplify. All variables represent nonzero real numbers.
66. ( ) ⁴
2zy²

Section 4.2 - Integral Exponents
Evaluate each expression.
40. W ⁻⁴
W ⁻⁶

Section 4.3 - addition of polynomials
Perform the indicated operation
48. (w² - 2w + 1) + (2w - 5 + w²)

Section 4.4 - Multiplying polynomials
Find each product
34. (3c²d - d³ + 1)8cd²

Section 4.5 - The FOIL Method
Use FOIL to find each product.
28. (11x + 3y) (x + 4y)

Section 4.6 - Product of sum and difference
Find each product
48. (3y² + 1) (3y² - 1)

Section 4.7 - Dividing a Polynomial by a Monomial
Find the quotients
26. 5y - 10
-5

Discussion Questions -

In drag racing, both vehicles begin at a dead stop, and then accelerate through 1/4 mi. Let us say, for the sake of discussion, that our two vehicles are not quite matched in power. That is, vehicle A can accelerate from 0 mph to 60 mph in 5 secs. Whereas the vehicle B can accelerate from 0 mph to 60 mph in 4 secs.

DQ 1: So, the question arises, how would you calculate the position of each vehicle after t secs? For instance, t = 5 or t = 6. Note: remember to convert from miles per hour to miles per second.
DQ 2: How would you determine the distance between the two vehicles after t secs?
DQ 3: How would you determine the time, t, for the fastest vehicle to traverse 1/4 mi.?
DQ 4: In the Indianapolis 500, the vehicles do not begin at a dead stop. In fact, a pace car sets the initial velocity; let us say it is 80 mph. If the lead vehicle can accelerate 0 to 100 mph in 5 secs, what would be the position of the lead vehicle from the starting point after t secs, for instance, t = 5 or t = 6?
DQ 5: What is the difference between a term and a factor?
DQ 6: Under which arithmetic operations on polynomials do you use the distributive law?
DQ 7: Which arithmetic operations on polynomials are associated with coefficients?
DQ 8: Which arithmetic operations on polynomials are associated with exponents?