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Question
State division algorithm for polynomials.
Solution
If f (x) and g (x) are any two polynomials with `g (x ) ≠ 0 `then we can always find polynomials ` q(x)` and `r (x)` such that `f (x)= q(x)g(x)+ r(x)`, where `r (x) = 0` or degree r(x) degree g(x)
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Case Study -1
The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.
Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t2 + 8t + k.
Rita’s height (in feet) above the water level is given by another polynomial p(t) with zeroes -1 and 2. Then p(t) is given by ______.
Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.
The shape of the path traced shown is:
`sqrt(2)` is a polynomial of degree ______.
Classify the following as a constant, linear, quadratic and cubic polynomials:
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