Question

Jennifer has carpet in her square bedroom. She decides to also purchase carpet for her living room which is rectangular in shape and 9 feet longer than her bedroom. The area of the carpet required in the living room is given by the quadratic expression below, where x represents the side length, in feet, of the carpet in the bedroom. Match each part of the expression with what it represents. Tiles :

1 the width of the carpet in the living room
2  the length of the carpet in the living room
3  the area of the carpet in the bedroom
4  the increase in the area of carpet needed for the living room
Pairs :
1 the second-degree term of the expression x2 + 9x
2  the monomial, x, a factor of the expression x2 + 9x
3  the first-degree term of the expression x2 + 9x
4   the binomial, (x + 9), a factor of the expression x2 + 9x

Answer 1

1. the width of the carpet in the living room

Ans. The monomial, x, a factor of the expression x2 + 9x

2 the length of the carpet in the living room

Ans . the binomial, (x + 9), a factor of the expression x2 + 9x

3 the area of the carpet in the bedroom

Ans. the second-degree term of the expression x2 + 9x

4. the increase in the area of carpet needed for the living room

Ans. the first-degree term of the expression x2 + 9x

Explanation:

Jennifer has carpet in her square bedroom.

Formula of area of square =
`a^2`

Where a is the side length

Side length of her bedroom is x

Area of the bedroom is
`x^2`

So, area of carpet for bedroom is
`x^2`

She decides to also purchase carpet for her living room which is rectangular in shape and 9 feet longer than her bedroom. (no change in width)

So, length of living room = 9+x

Width = x

Area of living room =
`x*(9+x)`

`=x^(2) +9x`

So, increase in area of carpet for living room in comparison to the area of carpet for bedroom is 9x

1. the width of the carpet in the living room

Ans. The monomial, x, a factor of the expression x2 + 9x

2 the length of the carpet in the living room

Ans . the binomial, (x + 9), a factor of the expression x2 + 9x

3 the area of the carpet in the bedroom

Ans. the second-degree term of the expression x2 + 9x

4. the increase in the area of carpet needed for the living room

Ans. the first-degree term of the expression x2 + 9x