Factor the following quadratic expressions. Use a visual model to assist you as needed. 12. \( 4 x^{2}+19 x-5 \) 13. \( 3 x^{2}-10 x+8 \) 14. \( 6 x^{2}+x-2 \) 15. \( 3 x^{2}-14 x-24 \) 16. \( 2 x^{2}+9 x+10 \) 17. \( 5 x^{2}+31 x+6 \) 18. \( 5 x^{2}+7 x-6 \) 19. \( 4 x^{2}+8 x-5 \)

For the quadratic \( 4x^2 + 19x - 5 \), we can factor it as \( (4x - 1)(x + 5) \). To see this visually, consider a rectangle where the area is represented by the expression. Split it into parts where one side can be \( 4x - 1 \) and the other can be \( x + 5 \), capturing the dimensions that multiply to give you the original expression. Meanwhile, for \( 3x^2 - 10x + 8 \), it factors to \( (3x - 4)(x - 2) \). If you visualize this, imagine you have a shape where two sections represent the two factors. The area of each rectangle can help you understand how the components combine to result in the original quadratic!