Write the following function in Scheme/DrRacket! Please do not use loops, as loops are not native to Scheme/DrRacket R5RS. Instead, use case analysis and recursion.

(8 points) A single-variable polynomial of degree n is written as where a a are coefficients. Suppose we represent such a polyno mial as a list (ao, a1, a2an In this question, you are asked to write a Scheme function polyMult that performs polynomial multiplication of two polynomials. For in- stance, when given (1 2 1) and (1 2 1), polyMult should return (1 4 6 4 1), because (1+2x +z?)(1 + 2x + x*) = 1 + 4x + 6x2 +4x3 +x4 We are going to implement the polynomial multiplication by convert- ing it into a series of polynomial addition operations. For the example, the multiplication can be performed in the following way: (1222 a2) (1 + 2x + x2)+ (0+02) (122 (122(1 2+a2) = 1+4x + 6x2 + 4x3 + x4 = Do the following steps to implement the above polynomial multiplica- tion procedure (a) Write a function nzero, which takes a number n and returns a list of n zeros. For instance, calling nzero on 3 returns (0 0 0) (b) Write a polynomial addition function polyAdd that adds two polynomials. For instance, when given (1 2 1) and (0 2 4 2), it returns (1 4 5 2) (8 points) A single-variable polynomial of degree n is written as where a a are coefficients. Suppose we represent such a polyno mial as a list (ao, a1, a2an In this question, you are asked to write a Scheme function polyMult that performs polynomial multiplication of two polynomials. For in- stance, when given (1 2 1) and (1 2 1), polyMult should return (1 4 6 4 1), because (1+2x +z?)(1 + 2x + x*) = 1 + 4x + 6x2 +4x3 +x4 We are going to implement the polynomial multiplication by convert- ing it into a series of polynomial addition operations. For the example, the multiplication can be performed in the following way: (1222 a2) (1 + 2x + x2)+ (0+02) (122 (122(1 2+a2) = 1+4x + 6x2 + 4x3 + x4 = Do the following steps to implement the above polynomial multiplica- tion procedure (a) Write a function nzero, which takes a number n and returns a list of n zeros. For instance, calling nzero on 3 returns (0 0 0) (b) Write a polynomial addition function polyAdd that adds two polynomials. For instance, when given (1 2 1) and (0 2 4 2), it returns (1 4 5 2)