jenna constructs the model to represent 3x² + 11x - 4. what factors does jenna need to model for the sides…

jenna constructs the model to represent 3x² + 11x - 4. what factors does jenna need to model for the sides? (3x + 1) and (x - 4) (3x - 1) and (x + 4) (3x - 2) and (x + 2) (3x + 2) and (x - 2)

jenna constructs the model to represent 3x² + 11x - 4. what factors does jenna need to model for the sides? (3x + 1) and (x - 4) (3x - 1) and (x + 4) (3x - 2) and (x + 2) (3x + 2) and (x - 2)

Answer

Explanation:

Step1: Factor the quadratic expression

We use the AC - method for factoring (ax^{2}+bx + c) (here (a = 3), (b=11), (c=-4)). Calculate (a\times c=3\times(-4)=-12). We need to find two numbers that multiply to (-12) and add up to (11). The numbers are (12) and (-1). Rewrite the middle - term: (3x^{2}+12x - x - 4).

Step2: Group the terms

((3x^{2}+12x)-(x + 4)).

Step3: Factor out the greatest common factor from each group

From (3x^{2}+12x), we factor out (3x) to get (3x(x + 4)), and from (-x - 4) we factor out (-1) to get (-1(x + 4)). So, (3x(x + 4)-1(x + 4)=(3x - 1)(x + 4)).

Answer:

B. ((3x - 1)) and ((x + 4))