Questions: Complete the following factorization. 3x^2+5x+2 factor as (3x+2)(...)

Transcript text: Complete the following factorization. \[ 3 x^{2}+5 x+2 \text { factor as }(3 x+2)(\ldots) \]

Solution

Solution Steps

To factor the quadratic expression \(3x^2 + 5x + 2\), we need to find two binomials that multiply together to give the original expression. We can use the method of splitting the middle term or directly use a factorization function from a math library.

Step 1: Identify the Quadratic Expression

We start with the quadratic expression given by \[ 3x^2 + 5x + 2. \]

Step 2: Factor the Expression

To factor the expression, we look for two binomials that multiply to give the original quadratic. The factorization results in: \[ (3x + 2)(x + 1). \]

Step 3: Verify the Factorization

To ensure the factorization is correct, we can expand the factors: \[ (3x + 2)(x + 1) = 3x^2 + 3x + 2x + 2 = 3x^2 + 5x + 2. \] This confirms that our factorization is accurate.