Set y = 0: x^2 - 4 = 0. Factoring gives (x - 2)(x + 2) = 0. Thus, x = 2 and x = -2.

First, factor out the common term 2: 2(x^2 + 4x + 3). Then, factor the quadratic: 2(x + 3)(x + 1).

To factor 2x^2 - 8, first factor out 2: 2(x^2 - 4). Then, recognize x^2 - 4 as a difference of squares: 2(x - 2)(x + 2).

First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 3(x - 2)(x + 2).

The expression 4x^2 - 12x + 9 is also a perfect square trinomial. It factors to (2x - 3)(2x - 3) or (2x - 3)^2.

First, factor out the greatest common factor, which is 4. This gives us 4(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 4(x - 2)(x + 2).

We need two numbers that multiply to -12 and add to 4. The numbers 6 and -2 work. Thus, the factored form is (x + 6)(x - 2).

The expression x^2 - 4 is a difference of squares. It factors to (x - 2)(x + 2).

First, we can factor out the greatest common factor, which is 2x. This gives us 2x(x + 4).

The expression 4x^2 - 25 is a difference of squares. It can be factored as (2x - 5)(2x + 5).

We need two numbers that multiply to -10 and add to 3. The numbers 5 and -2 work. Thus, the factorization is (x + 5)(x - 2).

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

To factor x^2 + 7x + 10, we need two numbers that multiply to 10 and add to 7. The numbers 2 and 5 work. Thus, the factorization is (x + 2)(x + 5).

To factor x^2 - 5x + 6, we look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factorization is (x - 2)(x - 3).

The expression x^2 - 9 is a difference of squares. It can be factored as (x - 3)(x + 3).

Factor out the common term 2: 2(x^2 - 4) = 2(x - 2)(x + 2).

First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, factor x^2 - 4 as a difference of squares: 3(x - 2)(x + 2).

To factor, we look for two numbers that multiply to 10 and add to 7. The numbers are 5 and 2. Thus, the factorization is (x + 5)(x + 2).

To factor x^2 - 5x + 6, we look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factorization is (x - 2)(x - 3).

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

First, factor out the common term x: x(x^2 - 3x - 4). Now, factor the quadratic x^2 - 3x - 4 to get x(x - 4)(x + 1).

Factor out the common term 3x: 3x(x + 4).

We need two numbers that multiply to 10 and add to 7. The numbers 5 and 2 work. Thus, the factored form is (x + 5)(x + 2).

To factor x^2 - 5x + 6, we need two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factorization is (x - 2)(x - 3).

Using the section formula: P = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (3, 4).

Using the section formula: P = ((1*9 + 1*3)/(1+1), (1*10 + 1*4)/(1+1)) = (6, 7).

Using the section formula: (mx2 + nx1)/(m+n), (my2 + ny1)/(m+n) where m=1, n=3. Coordinates = ((1*3 + 3*1)/(1+3), (1*8 + 3*2)/(1+3)) = (2, 6).

Using the section formula: (mx2 + nx1)/(m+n), (my2 + ny1)/(m+n) = (1*3 + 3*1)/(1+3), (1*4 + 3*2)/(1+3) = (3 + 3)/4, (4 + 6)/4 = (6/4, 10/4) = (1.5, 2.5).

Using the section formula: P(x, y) = ((2*3 + 1*1)/(2+1), (2*4 + 1*2)/(2+1)) = (2.67, 3.33).

Using the section formula: P = ((2*5 + 1*1)/(2+1), (2*6 + 1*2)/(2+1)) = (3, 4).