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?

Question

A) 2x^2 - 8 square feet
B) 6x^2 + 14x -8 square feet
C) 2x^2 + 2 square feet
D) 2x^2 - 14x - 8 square feet

Answer 1

To find the remaining area of Alex's workshop after renting part of it to Matt, we need to subtract the area that Matt is using from the total area of the workshop.

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

The area that Matt is renting is: \[ 2x^2 + 7x - 5 \]

We need to perform the subtraction: \[ (4x^2 + 7x - 3) - (2x^2 + 7x - 5) \]

Distributing the negative sign in the second expression, we get: \[ 4x^2 + 7x - 3 - 2x^2 - 7x + 5 \]

Now, combine like terms:

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

Putting it all together, we have: \[ 2x^2 + 0 + 2 = 2x^2 + 2 \]

Therefore, the expression that models the remainder of Alex's workshop space once he rents part of it to Matt is: \[ \boxed{2x^2 + 2} \]

So the correct answer is C) 2x^2 + 2 square feet.