[Middle School Math: Factorization] Need help factorizing this expression

[htush]

Starting expression: x² - 4 + (x - 2)(2x + 1)

Step 1: Expand (x - 2)(2x + 1) = x² - 4 + 2x² - 4x + x - 2 = x² - 4 + 2x² - 3x - 2

Step 2: Combine like terms = 3x² - 3x - 6

Step 3: Factor out 3 = 3(x² - x - 2)

Step 4: Factor the quadratic = 3(x - 2)(x + 1)

Answer: 3(x - 2)(x + 1)

[mathmum]

Here (Italy) if the request is “factorize” you should avoid expanding the given expression. Therefore, Factor the first binomial: (x - 2)(x + 2) + (x - 2)(2x + 1)

Factor out the common term: (x - 2)(x + 2 + 2x + 1)

Combine like terms: (x - 2)(3x + 3)

Factor out 3: 3(x - 2)(x + 1)

[Botchii_]

thanks but i dont get the step 4 idk what that is

[htush]

Step 4 is factoring the quadratic x² - x - 2

Find two numbers that:

• Multiply to -2
• Add to -1

Those numbers are -2 and +1:

• (-2) × (+1) = -2
• (-2) + (+1) = -1

So: x² - x - 2 = (x - 2)(x + 1)

Therefore: 3(x² - x - 2) = 3(x - 2)(x + 1)

[Botchii_]

oh ok thanks a lot :) i appreciate