Academy Algebra II 5.7: Apply the Fundamental Theorem of Algebra
... Fundamental Theorem of Algebra • If f(x) is a polynomial with degree of n (where n>0), then the equation f(x) = 0 has at least one solution. • Corollary: The equation f(x) = 0 has exactly n solutions provided each solution repeated twice is counted as 2 solutions, each solution repeated three times ...
... Fundamental Theorem of Algebra • If f(x) is a polynomial with degree of n (where n>0), then the equation f(x) = 0 has at least one solution. • Corollary: The equation f(x) = 0 has exactly n solutions provided each solution repeated twice is counted as 2 solutions, each solution repeated three times ...
A Method to find the Sums of Polynomial Functions at Positive
... out with the leading term of the polynomial Sp (n − 1), leaving a polynomial of degree t − 1. Since Ct 6= 0, the leading coefficient tCt is non-zero, so the degree of the resulting polynomial must be t − 1. Since Sp (n)−Sp (n−1) equals np , we know that this polynomial is of degree p. Thus, t − 1 = ...
... out with the leading term of the polynomial Sp (n − 1), leaving a polynomial of degree t − 1. Since Ct 6= 0, the leading coefficient tCt is non-zero, so the degree of the resulting polynomial must be t − 1. Since Sp (n)−Sp (n−1) equals np , we know that this polynomial is of degree p. Thus, t − 1 = ...
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