Question

factor $3x^2 + 5x - 12$.
a. $3(x + 1)(x - 4)$
b. $3(x - 1)(x + 4)$
c. $(x + 3)(3x - 4)$
d. $(x - 3)(3x + 4)$

Explanation:

Step1: Expand Option A

Expand \(3(x + 1)(x - 4)\): First multiply \((x + 1)(x - 4)=x^2-4x+x - 4=x^2-3x - 4\), then multiply by 3: \(3x^2-9x - 12\), not equal to \(3x^2 + 5x - 12\).

Step2: Expand Option B

Expand \(3(x - 1)(x + 4)\): First multiply \((x - 1)(x + 4)=x^2+4x - x - 4=x^2+3x - 4\), then multiply by 3: \(3x^2+9x - 12\), not equal to \(3x^2 + 5x - 12\).

Step3: Expand Option C

Expand \((x + 3)(3x - 4)\): Use FOIL method: \(x\times3x+x\times(-4)+3\times3x+3\times(-4)=3x^2-4x + 9x - 12=3x^2+5x - 12\), which matches the original expression.

Step4: Expand Option D (Optional)

Expand \((x - 3)(3x + 4)\): \(x\times3x+x\times4-3\times3x-3\times4=3x^2+4x - 9x - 12=3x^2-5x - 12\), not equal to \(3x^2 + 5x - 12\).

Answer:

C. \((x + 3)(3x - 4)\)