(3 points)

Question

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

Answer 1

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

1. Area covered by flower beds: \(3x^2 + 5x - 2\)
2. Area covered by vegetable plants: \(2x^2 - 3x + 4\)

Now, we will add these two expressions:

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

Combine like terms:

1. Combine the \(x^2\) terms: \[ 3x^2 + 2x^2 = 5x^2 \]

2. Combine the \(x\) terms: \[ 5x - 3x = 2x \]

3. Combine the constant terms: \[ -2 + 4 = 2 \]

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

\[ 5x^2 + 2x + 2 \text{ square feet} \]

So, in the required form:

\[ 5x^2 + 2x + 2 \text{ square feet} \]