Question

Factor the following trinomial: 6x2+11x+4 (1 point) Responses (2x+2)(3x+2) (2x+2)(3x+2) (3x+1)(2x+4) (3x+1)(2x+4) (2x+1)(3x+4) (2x+1)(3x+4) Not factorable.

Answer 1

To factor the trinomial \(6x^2 + 11x + 4\), we can look for two binomials of the form \((ax + b)(cx + d)\).

The first step is to identify the product \(ac = 6\) (the coefficient of \(x^2\)) and \(bd = 4\) (the constant term), while also ensuring that \(ad + bc = 11\) (the coefficient of \(x\)).

Let's evaluate the options provided:

1. **Option:** \( (2x + 2)(3x + 2) \)
- Product: \(2x \cdot 3x + 2 \cdot 2 + 2 \cdot 3x + 2 \cdot 2\)
- This simplifies to \(6x^2 + 10x + 4\) (not a match).

2. **Option:** \( (2x + 2)(3x + 2) \) (same as above, repeated, not a match).

3. **Option:** \( (3x + 1)(2x + 4) \)
- Product: \(3x \cdot 2x + 1 \cdot 4 + 3x \cdot 4 + 1 \cdot 2x\)
- This simplifies to \(6x^2 + 12x + 4\) (not a match).

4. **Option:** \( (3x + 1)(2x + 4) \) (same as above, repeated, not a match).

5. **Option:** \( (2x + 1)(3x + 4) \)
- Product: \(2x \cdot 3x + 1 \cdot 4 + 2x \cdot 4 + 1 \cdot 3x\)
- This simplifies to \(6x^2 + 8x + 3x + 4\)
- Which simplifies to \(6x^2 + 11x + 4\) (this is a match).

6. **Option:** Not factorable (incorrect, since we found a match).

Thus, the correct factorization of \(6x^2 + 11x + 4\) is:

\[
\boxed{(2x + 1)(3x + 4)}
\]