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+2 square feet 2 x squared plus 2 square feet 2x2−14x−8 square feet 2 x squared minus 14 x minus 8 square feet 6x2+14x−8 square feet 6 x squared plus 14 x minus 8 square feet 2x2−8 square feet 2 x squared minus 8 square feet

Answer 1

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

The total area of Alex's workshop is given by:
\[ 4x^2 + 7x - 3 \]

The area that Matt will use is given by:
\[ 2x^2 + 7x - 5 \]

Now we subtract Matt's area from Alex's area:
\[
(4x^2 + 7x - 3) - (2x^2 + 7x - 5)
\]

Distributing the subtraction across the terms gives:
\[
4x^2 + 7x - 3 - 2x^2 - 7x + 5
\]

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

Combining these, we get:
\[
2x^2 + 0 + 2 = 2x^2 + 2
\]

Thus, the expression that models the remainder of Alex's workshop space is:
\[ 2x^2 + 2 \text{ square feet} \]

The correct response is:
**2x^2 + 2 square feet**