Question

trinomial of (12x^2 - 13x + 3)

Explanation:

Assuming the problem is to factor the trinomial \(12x^2 - 13x + 3\).

Step 1: Find two numbers

We need two numbers that multiply to \(12\times3 = 36\) and add up to \(-13\). The numbers are \(-9\) and \(-4\) since \((-9)\times(-4)=36\) and \(-9 + (-4)=-13\).

Step 2: Rewrite the middle term

Rewrite \(-13x\) as \(-9x - 4x\) in the trinomial:
\(12x^2 - 9x - 4x + 3\)

Step 3: Group and factor

Group the first two terms and the last two terms:
\((12x^2 - 9x)+(-4x + 3)\)
Factor out the greatest common factor from each group:
\(3x(4x - 3)-1(4x - 3)\)

Step 4: Factor out the common binomial

Factor out \((4x - 3)\):
\((3x - 1)(4x - 3)\)

Answer:

\((3x - 1)(4x - 3)\)