Question

which factoring method would be used to factor $3x^2 - x - 4$?

grouping

sum/difference of cubes

ac method

difference of squares

perfect square

Explanation:

Step1: Analyze the quadratic form

The quadratic is \(3x^2 - x - 4\), which is in the form \(ax^2+bx+c\) with \(a = 3\), \(b=-1\), \(c = - 4\).

Step2: Evaluate each method

• Grouping: Usually for quadratics where we can split the middle term, but the AC method is more systematic for \(ax^2+bx + c\) with \(a

eq1\).

• Sum/Difference of Cubes: Applies to expressions like \(a^3\pm b^3\), not quadratics.
• AC Method: For \(ax^2+bx + c\), we find two numbers that multiply to \(a\times c\) and add to \(b\). Here, \(a\times c=3\times(-4)=-12\), and we need two numbers that multiply to \(-12\) and add to \(-1\) (the numbers are \(3\) and \(- 4\), since \(3\times(-4)=-12\) and \(3+(-4)=-1\)). This method is suitable.
• Difference of Squares: Applies to \(a^2 - b^2=(a - b)(a + b)\), not this quadratic.
• Perfect Square: Applies to \((a\pm b)^2=a^2\pm2ab + b^2\), this quadratic doesn't fit.

Answer:

C. AC Method