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Question

Can any one explain mr horner's method of synthetic division

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Solution

Dear Student,Horners method is a computationally efficient algorithm for evaluating a polynomial at a certain point or value. Given the polynomil, p(x) = i=0n ai xi = a0 + a1 x +.. + an xn, where an are real numbers, we wish to evaluate the polynomial at a specific value of x, say x0.To accomplish this, we define a new sequence of constants as follows: bn= an bn-1 :=an-1+bn x0 b0 :=a0+b1 x0 Then b0 is the value of p(x0). To see why this works, note that the polynomial can be written in the form p(x) = a0 + x(a1 + x(a2 +...+ x(an-1 + ax x)...)). Thus, by iteratively substituting the bi into the expression, p(x0)=a0+x0(a1+x0(a2+...+x0(an-1+bn x0)...)) =a0+x0(a1+x0(a2+...+x0(bn-1) ...)) =b0Regards

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