USING scheme

USING scheme

5. (8 points) A single-variable polynomial of degree n is written as where an,..., ao are coefficients. Suppose we represent such a polyno- mial as a list (ao, a1, a2, , an) 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 + 2r +226243+z 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 (12x +x2)(1 2r r2) (1 + 2x +x2)+ (0+2r +42)+ (0+0 + 2 2r3+) = 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 (O O 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)