Let's solve these quadratic expressions by factoring where possible.

1) $x^2 + 12x + 20$

We need two numbers that multiply to 20 and add up to 12.
These numbers are 10 and 2.
So, the factorization is:

$x^2 + 12x + 20 = (x + 10)(x + 2)$

3) $x^2 + 9x + 18$

We need two numbers that multiply to 18 and add up to 9.
These numbers are 6 and 3.
So, the factorization is:

$x^2 + 9x + 18 = (x + 6)(x + 3)$

4) $x^2 - 16x + 15$

We need two numbers that multiply to 15 and add up to $-16$.
These numbers are $-15$ and $-1$.
So, the factorization is:

$x^2 - 16x + 15 = (x - 15)(x - 1)$

5) $x^2 - 14x + 24$

We need two numbers that multiply to 24 and add up to $-14$.
These numbers are $-12$ and $-2$.
So, the factorization is:

$x^2 - 14x + 24 = (x - 12)(x - 2)$

6) $x^2 - 2x - 24$

We need two numbers that multiply to $-24$ and add up to $-2$.
These numbers are $-6$ and 4.
So, the factorization is:

$x^2 - 2x - 24 = (x - 6)(x + 4)$

7) $x^2 + 6x + 16$

We need two numbers that multiply to 16 and add up to 6.
However, there are no real numbers that satisfy this, so this expression cannot be factored using real numbers.
It does not factor over the reals, but you could use the quadratic formula to find complex roots.

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Would you like more details on any of these steps or further explanations?

Related Questions:

1. How do you use the quadratic formula to factor when it doesn’t factor normally?
2. What are common mistakes to avoid when factoring quadratics?
3. How do complex numbers factor into non-real quadratic factorizations?
4. What strategies help identify perfect squares in factoring?
5. How does completing the square help when factoring is not possible?

Tip: Always check your factorization by expanding the factors to verify the result matches the original quadratic.