(3 points)

Question

(3 points)
Maria is designing a garden for flowers and vegetables. The area of the garden covered by flower beds can be represented by the expression 3x2+5x−2
 square feet. The area of the garden covered by vegetable plants can be represented by the expression 2x2−3x+4
 square feet. What is the total area of both flowers and vegetables combined?

x2+

x+

square feet

GPT-4o mini · Answer

To find the total area of both the flowers and vegetables combined, we need to add the two expressions representing their areas:

Area covered by flower beds: $3 x^{2} + 5 x - 2$
Area covered by vegetable plants: $2 x^{2} - 3 x + 4$

Now, we will add these two expressions:

$(3 x^{2} + 5 x - 2) + (2 x^{2} - 3 x + 4)$

Combine like terms:

Combine the $x^{2}$ terms: $3 x^{2} + 2 x^{2} = 5 x^{2}$
Combine the $x$ terms: $5 x - 3 x = 2 x$
Combine the constant terms: $- 2 + 4 = 2$

Putting it all together, the total area of both flowers and vegetables combined is:

$5 x^{2} + 2 x + 2 square feet$

So, in the required form:

$5 x^{2} + 2 x + 2 square feet$