Question

he trinomial: $3x^2 + 8x + 4$

Explanation:

Step1: Factor the trinomial

We use the method of splitting the middle term. For the trinomial \(3x^{2}+8x + 4\), we need to find two numbers that multiply to \(3\times4 = 12\) and add up to \(8\). The numbers are \(6\) and \(2\) since \(6\times2=12\) and \(6 + 2=8\).
So we rewrite the middle term:
\(3x^{2}+6x+2x + 4\)

Step2: Group the terms

Group the first two terms and the last two terms:
\((3x^{2}+6x)+(2x + 4)\)

Step3: Factor out the common factors

Factor out \(3x\) from the first group and \(2\) from the second group:
\(3x(x + 2)+2(x + 2)\)

Step4: Factor out the common binomial factor

Now we can factor out \((x + 2)\) from both terms:
\((3x + 2)(x + 2)\)

Answer:

\((3x + 2)(x + 2)\)