Answer/Step-by-step explanation:
Let's highlight the dimensions of the bedroom and living room using the information given in the question:
==>Squared Bedroom dimensions:
Side length = w = x ft
Area = x*x = x²
==>Rectangular living room dimensions:
width = side length of the squared bedroom = x
length = (x + 9) ft
Area = L*W = x*(x+9) = x² + 9x
Now let's match each given expression with what they represent:
==>"the monomial, x, a factor of the expression x² + 9x" represents "the width of the carpet in the living room"
As we have shown in the dimensions of the squared bedroom above.
==>"the binomial, (x + 9), a factor of the expression x² + 9x" represents "the length of the carpet in the living room" as shown above in the dimensions for living room
==>"the second-degree term of the expression x² + 9x" represents "the area of the carpet in the bedroom"
i.e. the 2nd-degree term in the expression is x², which represents the area of the carpet of the given bedroom.
==>"the first-degree term of the expression x2 + 9x" represents "the increase in the area of carpet needed for the living room".
i.e. 1st-degree term in the expression is 9x. And it represents the increase in the area of the carpet for the living room. Area of bedroom is x². Area of carpet needed for living room increased by 9x. Thus, area of carpet needed for living room = x² + 9x
