Question

There is a more efficient algorithm (in terms of the number of multiplications and additions used) for evaluating polynomials than the conventional algorithm described in the previous exercise. It is called Horner's method. This pseudocode shows how to use this method to find the value of an​xn+an−1​xn−1+⋯+a1​x+a0​ at x=c procedure Horner (c,a0​,a1​,a2​,…,an​: real numbers)

y:=an​ for i:=1 to n
y:=y∗c+an−i​
return y{y=an​cn+an−1​cn−1+⋯+a1​c+a0​}
Evaluate 3x2+x+1 at x=2 by working through each step of the algorithm showing the values assigned at each assignment step.

Answer 1

Horner's method is a more efficient algorithm for evaluating polynomials by reducing the number of multiplications and additions. By applying Horner's method to the given polynomial, the value at x = 2 is found to be 13.

Step-by-step explanation:

Horner's method is a more efficient algorithm for evaluating polynomials. It reduces the number of multiplications and additions required. To evaluate a polynomial at a specific value, such as 3x^2 + x + 1 at x = 2, you can use Horner's method.

In Horner's method, you start with the highest degree term, multiply it by the value of x, and then add the next coefficient. You repeat this process until you reach the constant term. The final result is the value of the polynomial at the given x value.

In this case, starting with the highest degree term which is 3x^2, we multiply it by 2 and add the next coefficient, which is 1. The result is 13. Therefore, the value of the polynomial 3x^2 + x + 1 at x = 2 is 13.