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Ratanak
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P(x) is polynomial of degree 2012, P(k)=2^k, k=0,1,...,2012. Find P(2013)
The degree of a polynomial is the highest power of its variable. In this case, the degree of P(x) is 2012.
The coefficient of x^2013 in P(x) is the number multiplied to x^2013. This can be found by looking at the term in the polynomial that contains x^2013. If there is no term with x^2013, then the coefficient is 0.
To calculate P(2013), simply plug in the value of 2013 for x in the polynomial P(x) and then simplify the resulting expression. This will give you the value of P(2013).
The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In this case, the leading coefficient of P(x) is the coefficient of x^2012.
Calculating P(2013) allows us to find the value of the polynomial at a specific point, in this case, x = 2013. This can be useful in various applications, such as finding the roots or zeros of the polynomial or analyzing its behavior at that particular point.