Question Factor completely. \[ 6 x^{2}+19 x+3 \]

To factor the expression \( 6x^2 + 19x + 3 \), we need two numbers that multiply to \( 6 \times 3 = 18 \) and add to \( 19 \). The numbers \( 18 \) and \( 1 \) fit the bill! We can rewrite the middle term \( 19x \) as \( 18x + 1x \), giving us \( 6x^2 + 18x + 1x + 3 \). Now, we can factor by grouping: \[ 6x(x + 3) + 1(x + 3) \] Now, factor out the common factor \((x + 3)\): \[ (6x + 1)(x + 3) \] So, the completely factored form is \( (6x + 1)(x + 3) \). A little side note—factoring is like detective work! You’re on the hunt for numbers that fit perfectly together, making every puzzle piece click into place. It’s all about finding those relationships, much like solving a mystery! If you're ever tackling higher-degree polynomials, don’t forget the good ol' quadratic formula. While factoring is great when you can, the formula can swoop in to save the day when the numbers get extra tricky—always keep it in your back pocket!