First, factor out 3: 3(x^2 - 4). Then, factor the difference of squares: 3(x - 2)(x + 2).

Step 1: Find two numbers that multiply to 6 and add to 5: 2 and 3. Step 2: Factor: (x + 2)(x + 3).

Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Factor as (x + 5)(x + 2).

To factor, we look for two numbers that multiply to 24 and add to -10. The numbers -4 and -6 work, so the factored form is (x - 4)(x - 6).

This is a difference of squares: x^2 - 4^2 = (x - 4)(x + 4).

This is a difference of squares: x^2 - 4 = (x - 2)(x + 2).

The polynomial x^2 - 6x + 9 can be factored as (x - 3)(x - 3) or (x - 3)^2.

Step 1: Recognize it as a difference of squares: x^2 - 3^2. Step 2: Factor: (x - 3)(x + 3).

This quadratic can be factored as (x + 3)(x + 3) or (x + 3)^2.

Step 1: Find two numbers that multiply to 6 and add to -5: -2 and -3. Step 2: Write the factors: (x - 2)(x - 3).

To factor, we look for two numbers that multiply to 10 and add to -7. The numbers -2 and -5 work, so the factored form is (x - 2)(x - 5).

The expression x^2 - 9 is a difference of squares, which factors to (x - 3)(x + 3).

Find two numbers that multiply to 6 and add to -5: -2 and -3. Thus, (x - 2)(x - 3).

This is a perfect square trinomial. It factors to (x + 2)(x + 2) or (x + 2)^2.

The expression x^2 + 6x + 9 is a perfect square trinomial. It factors to (x + 3)(x + 3) or (x + 3)^2.

Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Write in factored form: (x + 5)(x + 2).

The expression x^2 - 4 is a difference of squares and can be factored as (x - 2)(x + 2).

The polynomial factors to (x - 2)(x - 3) since the roots are 2 and 3.

This is a difference of squares: x^2 - 9 = (x - 3)(x + 3).

The leading coefficient is the coefficient of the term with the highest degree. Here, it is 4.

The leading coefficient is the coefficient of the term with the highest degree. Here, the leading term is 4x^3, so the leading coefficient is 4.

Step 1: Use the distributive property: x^2 + 4x + x + 4. Step 2: Combine like terms: x^2 + 5x + 4.

Step 1: Use the distributive property: x^2 - 3x + 2x - 6 = x^2 - x - 6.

The product of the roots of a quadratic equation ax^2 + bx + c = 0 is given by c/a. Here, 2/1 = 2.

The product of the roots is given by c/a. Here, c = 3, so the product is 3.

Step 1: Use the formula c/a. Here, c = 2 and a = 1, so the product is 2/1 = 2.

Step 1: Use the product of roots formula c/a. Here, c = 6, a = 1. Step 2: Product = 6/1 = 6.

Step 1: Use the formula c/a. Step 2: Here, c = 8 and a = 1. Step 3: Product of roots = 8.

The vertex is at (0, 4) and opens downwards, so the range is y ≤ 4.

Step 1: Use the distributive property: 2x^2 - 2x + 3x - 3. Step 2: Combine like terms: 2x^2 + x - 3.