Question

Consider the polynomial p(x) = a0 + a1x + a2x2 + a3x3 , where ai 0 i. The minimum number of multiplications nee

Answer 1

Accoridng to the Horner’s rule the division of an algorithm to a simple for the process by evaluating with a polynomial f(x) with an absolute value of x=x0 by diving with many monomials.

They have to obtain the next forth to an accumulative with an addition fashion to re-write polynomials to add the results for next monomials.

P(x)= a0 + a1x + a2x^2 + a3x^3

P(x)= a0 +(( a1+a2x + a3x^2) x )  ---------> Taking x common for 1 multiplications    

P(x)= a0 +(( a1+(a2 + a3x ) x ) x   ----------> multipication with a in an inner bracket

P(x)= a0 +( ( a1+(a2 + a3x ) x ) x )  ---------> Multiplications with an entire bracket