Question

Two polynomials in the variable x are represented by the coefficient vectors p₁ = [6,2,7,-3] and p₂ = [10,-5,8].

a. Use MuPAD to find the product of these two polynomials; express the product in its simplest form.

b. Use MuPAD to find the numeric value of the product if x = 2.

Answer 1

a)

For defining the polynomial in the variable x, we will first define a symbolic variable x. To define the polynomial with given coefficient vectors, we will use poly2sym function which will convert the polynomial expression to symbolic expression.

Input:

syms x %defining the symbolic variable x

p1=poly2sym([6,2,7,-3],x); %defining polynomial 1

p2=poly2sym([10,-5,8]) ; %defining polynomial 2

product=p1*p2; %finding the product

disp('product of two polynomial is: ')

disp(product) %displaying the product

disp('product of two polynomial in simplest form is: ')

disp(expand(product)) %using expand we can simplify the product

Output:

b)

For finding the value of product at x=2, we can use subs function which will substitute the variable x with 2 and compute the expression as follows,

Input:

syms x %defining the symbolic variable x

 

p1=poly2sym([6,2,7,-3],x); %defining polynomial 1

p2=poly2sym([10,-5,8]) ; %defining polynomial 2

product=p1*p2; %finding the product

val=subs(product,2); %substituting x=2 to the product

disp('The value of the product at x=2 is:')

disp(val)

Output:

a) For defining the polynomial in the variable x, we will first define a symbolic variable x.

b)

For finding the value of product at x=2, we can use subs function which will substitute the variable x with 2 and compute the expression as follows,