which expression is a factor of 12x² + 29x - 8?\no x - 8\no 2x - 1\no 3x + 8\no 4x + 1

Explanation:

Step1: Use the AC - method

For the quadratic expression (ax^{2}+bx + c=12x^{2}+29x - 8), where (a = 12), (b = 29), (c=-8). Calculate (ac=12\times(-8)=-96). We need to find two numbers that multiply to (-96) and add up to (29). The numbers are (32) and (- 3) since (32\times(-3)=-96) and (32+( - 3)=29).

Step2: Rewrite the middle - term

Rewrite (12x^{2}+29x - 8) as (12x^{2}+32x-3x - 8).

Step3: Group the terms

((12x^{2}+32x)-(3x + 8)=4x(3x + 8)-1(3x + 8)).

Step4: Factor by grouping

((3x + 8)(4x-1)).

Answer:

C. (3x + 8)