What are the steps to factor the expression x² + 2x – 3?

To factor the quadratic expression x² + 2x – 3, you’ll want to follow these steps:

1. Identify the coefficients: In the expression x² + 2x – 3, the coefficients are as follows:
• A (the coefficient of x²) = 1
• B (the coefficient of x) = 2
• C (the constant term) = -3
2. Find two numbers that multiply to AC: First, calculate AC = A * C, which in this case is:
• AC = 1 * (-3) = -3

Now, we need to find two numbers that multiply to -3 and add up to 2 (the coefficient B). The numbers that work are:

• 3 and -1
3. Rewrite the middle term: Now, rewrite the expression by splitting the 2x into 3x and -1x:

This gives us:

x² + 3x – 1x – 3

4. Factor by grouping: Next, we can group the terms:
• (x² + 3x) + (-1x – 3)

Now factor out the common factors from each group:

• x(x + 3) – 1(x + 3)
5. Combine the factors: Since both groups share a common factor of (x + 3), we can factor this out:

(x + 3)(x – 1)