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    Algebra: Multiplying and adding polynomials

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    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?

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    https://brainmass.com/math/basic-algebra/223960

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    Operations with polynomials

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