When the numerator or denominator are given in a factorized form, we need to multiply polynomials. Although this can be done by hand, MATLAB provides the function convthat computes the coefficients of the polynomial resulting from the product of two polynomials.

(a) Use helpin MATLAB to find how convcan be used, and then consider two polynomials

P(s) = s² + s + 1 and Q(s) = 2s³ + 3s² + s + 1

do the multiplication of these polynomials by hand to find Z(s) = P(s) Q(s) and use convto verify your results.

(b) The output of a system has a Laplace transform

use convto find the denominator polynomial and then find the inverse Laplace transform using ilaplace.

N(s) Y (s) D(s) (s + 2) .2. s(s + 1)((s+ 4)² + 9)