There is a more efficient algorithm (in terms of the number of multiplications and additions used)...

 

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There is a more efficient algorithm (in terms of the number of multiplications and additions used) for evaluating polynomials than the conventional algorithm It is called Horner's method. The pseudocode shows how to use Horner method to find the value of anxn+an-1xn−1 + · ... +a1xao at x = c. procedure Horner (c, a0, a1, ., an: real numbers) y = an for 1 to n y=ycan-i {y=anch+an-1cn-1 + (a) (b) ... +α₁c + ao} Evaluate 3x² + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. Exactly how many multiplications and additions are used by this algorithm to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.) There is a more efficient algorithm (in terms of the number of multiplications and additions used) for evaluating polynomials than the conventional algorithm It is called Horner's method. The pseudocode shows how to use Horner method to find the value of anxn+an-1xn−1 + · ... +a1xao at x = c. procedure Horner (c, a0, a1, ., an: real numbers) y = an for 1 to n y=ycan-i {y=anch+an-1cn-1 + (a) (b) ... +α₁c + ao} Evaluate 3x² + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. Exactly how many multiplications and additions are used by this algorithm to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.)