finding the product of a monomial and a binomial.

Question

How is the degree of the product related to the degree of the monomial and the degree of the binomial? Please give examples and explain.

Answer 1

You will need to look that highest exponent of the variable in the monomial and the highest exponent of variable in the binomial.  When you add the highest exponent from the monomial and binomial (because we are multiplying the monomial and binomial), you get the degree of the product.

 

x³  ---> monomial  (expression with one term)

 

x⁶ + x⁵  ----> binomial (expression with 2 terms)

 

 

x³ and x⁶ are terms with the highest exponent.  So if we add the exponents, we get 9.  The degree is 9.

 

Now we can multiply the monomial by the binomial from our example.

 

x³(x⁶ + x⁵) = x⁹ + x⁸

 

 

The degree is still 9.