What is the fully factored form of 3x^2 - 12x - 36?

What is the fully factored form of 3x^2 - 12x - 36?

• A. 3 (x - 6)(x + 2)
• B. 3 (x^2 - 4x - 12)
• C. (3x - 12)(x + 3)
• D. 3x (x - 6)

Answer: (A)

When you see a quadratic, start by pulling out any common factor, then factor the remaining expression completely. Here, every term shares a factor of 3, so factor that out: 3(x^2 - 4x - 12). Now factor the trinomial x^2 - 4x - 12 by finding two numbers that multiply to -12 and add to -4. Those numbers are -6 and 2, giving (x - 6)(x + 2). Put it all together: 3(x - 6)(x + 2). This is the fully factored form because it’s a product of linear factors with no common factors left. Quick check by expanding: (x - 6)(x + 2) = x^2 - 4x - 12, and multiplying by 3 gives 3x^2 - 12x - 36, which matches the original expression. Other forms either don’t factor completely or produce a different expansion.

When you see a quadratic, start by pulling out any common factor, then factor the remaining expression completely. Here, every term shares a factor of 3, so factor that out: 3(x^2 - 4x - 12). Now factor the trinomial x^2 - 4x - 12 by finding two numbers that multiply to -12 and add to -4. Those numbers are -6 and 2, giving (x - 6)(x + 2). Put it all together: 3(x - 6)(x + 2). This is the fully factored form because it’s a product of linear factors with no common factors left.

Quick check by expanding: (x - 6)(x + 2) = x^2 - 4x - 12, and multiplying by 3 gives 3x^2 - 12x - 36, which matches the original expression. Other forms either don’t factor completely or produce a different expansion.