Factoring quadratics. Game on.

$x^{2} - 16$ is a difference of squares: $x^{2} - 4^{2}$. So $x^{2} - 16 = (x + 4)(x - 4)$.

The greatest common factor of $10x^{2}$ and $15x$ is $5x$. So $10x^{2} - 15x = 5x(2x - 3)$.

Two numbers that multiply to $12$ and add to $7$ are $3$ and $4$. So $x^{2} + 7x + 12 = (x + 3)(x + 4)$.

$x^{2} - 25$ is a difference of squares: $x^{2} - 5^{2}$. So $x^{2} - 25 = (x + 5)(x - 5)$.

The greatest common factor of $12x^{2}$ and $8x$ is $4x$. So $12x^{2} + 8x = 4x(3x + 2)$.

Two numbers that multiply to $-14$ and add to $-5$ are $-7$ and $2$. So $x^{2} - 5x - 14 = (x - 7)(x + 2)$.

Two numbers that multiply to $2$ and add to $-3$ are $-1$ and $-2$. So $x^{2} - 3x + 2 = (x - 1)(x - 2)$.

Two numbers that multiply to $-12$ and add to $-1$ are $3$ and $-4$. So $x^{2} - x - 12 = (x + 3)(x - 4)$.