Question

Alex has a workshop with an area that can be modeled by the expression 4x2+7x−3
square feet. He agrees to rent out part of his workshop to his friend Matt. Alex agrees to let Matt use a space in his workshop that is 2x2+7x−5
square feet.

What is the expression that models the remainder of Alex's workshop space once he rents Matt his portion?

(1 point)
Responses

2x2−8
square feet
2 x squared minus 8 square feet

6x2+14x−8
square feet
6 x squared plus 14 x minus 8 square feet

2x2+2
square feet
2 x squared plus 2 square feet

2x2−14x−8
square feet

Answer 1

To find the expression that models the remainder of Alex's workshop space after renting out part to his friend Matt, you need to subtract the area Matt is using from the total area of the workshop.

1. Total area of Alex's workshop: \( 4x^2 + 7x - 3 \)
2. Area rented to Matt: \( 2x^2 + 7x - 5 \)

Now, we can subtract the area rented to Matt from the total area:

\[
(4x^2 + 7x - 3) - (2x^2 + 7x - 5)
\]

Distributing the negative sign gives us:

\[
4x^2 + 7x - 3 - 2x^2 - 7x + 5
\]

Now, combine like terms:

- For \(x^2\): \(4x^2 - 2x^2 = 2x^2\)
- For \(x\): \(7x - 7x = 0\)
- For the constant terms: \(-3 + 5 = 2\)

Putting it all together, we have:

\[
2x^2 + 0x + 2 = 2x^2 + 2
\]

Thus, the expression that models the remainder of Alex's workshop space is:

\[
\boxed{2x^2 + 2} \text{ square feet}
\]

This corresponds with the response: **2x² + 2 square feet**.