Question

Alex has a workshop with an area that can be modeled by the expression 4x^2+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 2x^2+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

2x^2−8
square feet

2x^2−14x−8
square feet

2x^2+2
square feet

6x^2+14x−8
square feet

Answer 1

To find the expression that models the remainder of Alex's workshop space after renting out part of it to Matt, we can subtract the area Matt is using from the total area of the workshop.

1. Total area of the workshop: \(4x^2 + 7x - 3\)
2. Area Matt is using: \(2x^2 + 7x - 5\)

We can perform the subtraction as follows:

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

Now simplify the expression:

1. Distribute the negative sign:

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

2. Combine like terms:

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

Putting it all together, we get:

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

Therefore, the expression that models the remainder of Alex's workshop space once he rents Matt his portion is:

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