Answer to Question #189632 in Algebra for Bansari

Question

Evaluate the following polynomial expression using Horner’s rule. Assume the value of x

is 3.

𝑃(𝑥) = 10x⁵ + 6x⁴+ 3x³ − 6x² + 8𝑥 + 15

Show all the intermediate steps.

Answer 1

$\text{Given, the polynomial }p(x)=10x^5+6x^4+3x^3-6x^2+8x+15 and x_0=3\newline \text{Since, it is 5 degree polynomial.} n=5\newline Horner's rule,\newline 1. Set k = n\newline 2. Let b_k = a_k\newline 3. Let b_{k - 1} = a_{k - 1 }+ b_kx_0\newline 4. Let k = k - 1\newline 5. If k ≥ 0 \text{then go to step 3}\newline \text{Else End}\newline Then,\newline b_5=a_5=10\newline b_4 = a_4 + x_0b_5=6+3×10=36 \newline b_3 = a_3 + x_0b_4=3+3×36=111 \newline b_2 = a_2 + x_0b_3=-6+3×111=327 \newline b_1 = a_1 + x_0b_2=8+3×327=989 \newline b_0 = a_0 + x_0b_1=15+3×989=2982 \newline Therefore,P(3)=2982.$