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 2x27x5 square feet.
What is the expression that models the remainder of Alex's
workshop space once he rents Matt his portion?
(1 point)
2x2 8 square feet
2x22 square feet
2x² - 14x 8 square feet
6x2 +14x
-
8 square feet

Answer 1

To find the expression that models the remainder of Alex's workshop space after renting a portion to Matt, we need to subtract the area rented to Matt from the total area of Alex's workshop.

Given:
- Total area of workshop: \( 4x^2 + 7x - 3 \) square feet
- Area rented to Matt: \( 2x^2 + 7x + 5 \) square feet

Now, we perform the subtraction:

\[
\text{Remainder} = \text{Total area} - \text{Area rented to Matt}
\]

\[
\text{Remainder} = (4x^2 + 7x - 3) - (2x^2 + 7x + 5)
\]

Now, we distribute the negative sign:

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

Next, we combine like terms:

1. For \(x^2\) terms: \(4x^2 - 2x^2 = 2x^2\)
2. For \(x\) terms: \(7x - 7x = 0\)
3. For constant terms: \(-3 - 5 = -8\)

Putting this all together, we have:

\[
\text{Remainder} = 2x^2 - 8
\]

So, the expression that models the remainder of Alex's workshop space once he rents out part to Matt is:

**\(2x^2 - 8\) square feet.**