Chapter 8.2, Problem 44PPS

a.

To determine

To find: Degree of each product.

Explanation of Solution

Three possible monomials are $2x,3x^2,4x^3$ .

Three polynomials are $x^2-1,x^5+1,x^6+1$

The degree of the monomial is the sum of the exponents . For example given ,case they are $1,2$ and $3$

The degree of the polynomial is the largest degree of the monomials. For the example given, they are $2,5$ and $6$ .

Use the distributive property to find the product of the monomial and the polynomial.

For the example given they are $2x^3-2x,3x^7+3x^2$ and $4x^9+4x$ .

For the example given, the degree of the new polynomials are $3,7$ and $9$

Monomial	Degree	Polynomial	Degree	Product of Monomial and Polynomial	Degree
$2x$	$1$	$x^2-1$	$2$	$2x^3-2x$	$3$
$3x^2$	$2$	$x^5+1$	$5$	$3x^7+3x^2$	$7$
$4x^3$	$3$	$x^6+1$	$6$	$4x^9+4x$	$9$

b.

To determine

To find:What is the degree of the product of a monomial of degree $a$ and a polynomial of degree $b$ .

Answer to Problem 44PPS

The degree of the product is the sum of the degree of the monomial and the degree of the polynomial

Explanation of Solution

The degree of the product is the sum of the degree of the monomial and the degree of the polynomial , or $a+b$