Question

A) Evaluate the polynomial ( f(x)=x^{4}-2 x^{2}+3 x+11 ) using Homer's rule at ( x=4 ).

Answer 1

To evaluate the polynomial f(x)=x^{4}-2 x^{2}+3 x+11 using Horner's rule at x=4, we divide the coefficients by 4, multiply by x, and add the results. The final result is 10.

Step-by-step explanation:

To evaluate the polynomial f(x)=x^{4}-2 x^{2}+3 x+11 using Horner's rule at x=4, we need to follow these steps:

1. Start by dividing the polynomial by the value of x.
2. Next, take the result of the division and multiply it by the value of x. This will give you a new value.
3. Repeat steps 1 and 2 until you have evaluated the polynomial.

Let's work through these steps:

1. Divide 4 into the coefficient of the highest power term, which is 1.
   1/4 = 0.25
2. Multiply the result by the value of x, which is 4.
   0.25 * 4 = 1
3. Add the result to the next coefficient, which is -2.
   1 + (-2) = -1
4. Multiply the result by the value of x again.
   -1 * 4 = -4
5. Add the result to the next coefficient, which is 3.
   -4 + 3 = -1
6. Finally, add the constant term, which is 11.
   -1 + 11 = 10

Therefore, the polynomial evaluated at x = 4 using Horner's rule is 10.