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An object is dropped from the top of Pittsburgh's USX Towers, which is 841 feet tall. (Source: World Almanac research) The height of the object after seconds is given by the expression \(841-16 t^{2}\). a. Find the height of the object after 2 seconds. b. Find the height of the object after 5 seconds. c. To the nearest whole second, estimate when the object hits the ground. d. Factor \(841-16 t^{2}\).

At this writing, the world's tallest building is the Taipei 101 in Taipei, Taiwan, at a height of 1671 feet. (Source: Council on Tall Buildings and Urban Habitat) Suppose a worker is suspended 71 feet below the top of the pinnacle atop the building, at a height of 1600 feet above the ground. If the worker accidentally drops a bolt, the height of the bolt after tseconds is given by the expression \(1600-16 t^{2}\). a. Find the height of the bolt after 3 seconds. b. Find the height of the bolt after 7 seconds. c. To the nearest whole second, estimate when the bolt hits the ground. d. Factor \(1600-16 t^{2}\).

Explain how you can tell whether a polynomial is written in factored form.

A performer with the Moscow Circus is planning a stunt involving a free fall from the top of the Moscow State University building, which is 784 feet tall. (Source: Council on Tall Buildings and Urban Habitat) Neglecting air resistance, the performer's height above gigantic cushions positioned at ground level after \(t\) seconds is given by the expression \(784-16 t^{2}\) a. Find the performer's height after 2 seconds. b. Find the performer's height after 5 seconds. c. To the nearest whole second, estimate when the performer reaches the cushions positioned at ground level. d. Factor \(784-16 t^{2}\).

Construct a four-term polynomial that can be factored by grouping. Explain how you constructed the polynomial.