Question

using the x method to factor a trinomial

what is the factored form of (6x^2 + 13x + 6)?

(x + 4)(x + 9)
(2x + 3)(3x + 2)
(2x + 6)(3x + 1)
(6x + 1)(6x + 1)

Explanation:

Identify the coefficients of the trinomial

For the trinomial \(6x^2 + 13x + 6\), compare it to the standard form \(ax^2 + bx + c\):

$$ a = 6,\quad b = 13,\quad c = 6 $$

Apply the X method parameters

Find the product \(ac\) and the sum \(b\):

$$
LATEXBLOCK0
$$

We need two numbers that multiply to \(36\) and add to \(13\). These numbers are \(9\) and \(4\):

$$
LATEXBLOCK1
$$

Rewrite and factor by grouping

Rewrite the middle term \(13x\) as \(9x + 4x\) and factor by grouping:

$$
LATEXBLOCK2
$$

Answer:

• (A) \((x + 4)(x + 9)\)
• (B) \((2x + 3)(3x + 2)\) (Correct answer)
• (C) \((2x + 6)(3x + 1)\)
• (D) \((6x + 1)(6x + 1)\)