Having trouble answering these and also explaining why.. 1. Suppose \"p\" is a p

Question

Having trouble answering these and also explaining why.. 1. Suppose "p" is a polynomial of degree "n" and "q" is apolynomial of degree "m". Can you predict the degree ofp+q? 2. Suppose "p" is a polynomial of degree "n" and "q" is apolynomial of degree "m". Can you predict the degree of(p)(q)? 3. Suppose "r" is a rational function of relative degree "m"and "f" is a rational function of relative degree "n". Can youpredict the relative degree of r+f ? 1. Suppose "p" is a polynomial of degree "n" and "q" is apolynomial of degree "m". Can you predict the degree ofp+q? 2. Suppose "p" is a polynomial of degree "n" and "q" is apolynomial of degree "m". Can you predict the degree of(p)(q)? 3. Suppose "r" is a rational function of relative degree "m"and "f" is a rational function of relative degree "n". Can youpredict the relative degree of r+f ?

Explanation / Answer

1. In adding polynomials, the degree of the sum is the degreeof the highest-degree polynomial. So, if m > n, then the degreeof p+q is m, if m < n, then the degree of p+q is n. If m=n, thedegree of p + q is m or n. 2. The degree of the polynomial is dependent on the term withthe largest exponent. To get the exponent of the term with thelargest exponent in the polynomial pq, we add the degrees of p andq. And so, the degree of pq is m+n.

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