Factor. \[ \begin{array}{ll}x^{2}-4 x-21= & 3 x^{2}+4 x+1= \\ a^{2}-10 a+21= & 3 y^{2}+24 y-60= \\ x^{2}-8 x+16= & 10 x^{2}+17 x+3= \\ y^{2}-64= & x^{2}-4 x-60=\end{array} \]

Let's factor the expressions one by one with a touch of fun! 1. **\( x^{2} - 4x - 21 \)**: This quadratic can be factored by looking for two numbers that multiply to \(-21\) and add up to \(-4\). Those magical numbers are \(-7\) and \(3\). So, it factors to \((x - 7)(x + 3)\). 2. **\( 3x^{2} + 4x + 1 \)**: Here, we need to find two numbers that multiply to \(3 \cdot 1 = 3\) and add to \(4\). Luckily, those numbers are \(3\) and \(1\). So we can factor by grouping, giving us \(3x^{2} + 3x + x + 1 = (3x + 1)(x + 1)\). 3. **\( a^{2} - 10a + 21 \)**: For this expression, we want numbers that multiply to \(21\) and add to \(-10\). The perfect pair is \(-3\) and \(-7\). Thus, it factors to \((a - 3)(a - 7)\). 4. **\( 3y^{2} + 24y - 60 \)**: Looking for numbers that multiply to \(3 \cdot (-60) = -180\) and add to \(24\), we find that \(30\) and \(-6\) are the combination we need! This gives us \(3y^{2} + 30y - 6y - 60 = 3(y + 10)(y - 2)\). 5. **\( x^{2} - 8x + 16 \)**: Recognize that this is a perfect square! Both roots are \(4\) so it factors to \((x - 4)(x - 4)\) or simply \((x - 4)^{2}\). 6. **\( 10x^{2} + 17x + 3 \)**: We need two numbers that multiply to \(30\) and add to \(17\), which are \(15\) and \(2\). We can factor it as \(10x^{2} + 15x + 2x + 3 = (5x + 1)(2x + 3)\). 7. **\( y^{2} - 64 \)**: Ah, the classic difference of squares! This factors beautifully into \((y - 8)(y + 8)\). 8. **\( x^{2} - 4x - 60 \)**: For this one, we look for factors of \(-60\) that sum up to \(-4\). The numbers \(-10\) and \(6\) do the trick! Hence, it becomes \((x - 10)(x + 6)\). And there you have it—factoring can be so much fun! Time to impress your friends with your math wizardry!