Standard Representation: Simplify f(x) = (-x+2)(x+3)

To solve this problem, we'll follow these steps:

• Step 1: Use the FOIL method to expand the product of binomials.
• Step 2: Combine like terms to simplify the expression.

Now, let's work through each step:

Step 1: Expand the product $(-x+2)(x+3)$ using the FOIL method:
First terms: $-x \cdot x = -x^2$
Outer terms: $-x \cdot 3 = -3x$
Inner terms: $2 \cdot x = 2x$
Last terms: $2 \cdot 3 = 6$

This gives us the expression:
$-x^2 - 3x + 2x + 6$

Step 2: Combine like terms:
Combine $-3x$ and $2x$ to get $-x$.
Thus, the expression simplifies to:
$-x^2 - x + 6$

Therefore, the standard form of the function is $f(x) = -x^2 - x + 6$.