**The motion of an object that’s thrown 3m up at a velocity of 14 m/s can be described using the polynomial -5tsquared + 14t + 3 = 0.** Factorizing the quadratic equation gives the time it takes for the object to hit the ground. Polynomials apply in fields such as engineering, construction and pharmaceuticals.

If a 5,800-square-meter piece of land has a width that’s 15 m wider than its length, it’s possible to calculate its length and width by expressing the problem as a polynomial. Since the area of a rectangle is given by L x W, L (L+15) = 5800. Further manipulation gives L squared + 15L – 5800 = 0. On factoring, the equation becomes (L-80) (L+95) = 0. Thus, L+95 = 0 or L-80 = 0. Since length can’t be negative, L= 80m is the correct length for the piece of land.

If an operator reduces the bus fare by $0.25 for every additional passenger he gets, he has to figure out the point to stop doing that to remain profitable. If the fare for one passenger is $30, the profit can be expressed as P(x) = x (30 - 0.25 (x-1) or P(x) = -0.25 x squared + 30.25 x, where x is the number of passengers.