Can someone solve theses for me?

Factor the polynomial x2 + 7x + 12 completely

Factor the polynomial x2 – 4 completely

Factor the polynomial 18a2b – 4ab + 10a completely

x2 + 7x + 12 = (x+4)(x+3)
x2 – 4 = (x+2)(x-2)
18a2b – 4ab + 10a = 2a(9ab - 2b + 5)

Factor the following polynomial completely.

-x2y2 + x4 + 9y2 - 9x2

To factor the polynomial x^2 + 7x + 12 completely:

1. Find two numbers whose product is equal to the product of the coefficient of x^2 (which is 1) and the constant term (which is 12). In this case, the numbers are 3 and 4 because 3 * 4 = 12.
2. Rewrite the middle term 7x as the sum of these two numbers: 7x = 3x + 4x.
3. Group the terms: x^2 + 3x + 4x + 12.
4. Factor by grouping: (x^2 + 3x) + (4x + 12) = x(x + 3) + 4(x + 3).
5. Factor out the common factor: (x + 3)(x + 4).
Therefore, the factored form of x^2 + 7x + 12 is (x + 3)(x + 4).

To factor the polynomial x^2 – 4 completely:
1. Recognize that this is a difference of squares.
2. Rewrite the constant term -4 as a perfect square: -4 = (-2)^2.
3. Apply the formula for factoring a difference of squares: x^2 – 4 = (x – 2)(x + 2).
Therefore, the factored form of x^2 – 4 is (x – 2)(x + 2).

To factor the polynomial 18a^2b – 4ab + 10a completely:
1. Recognize that all three terms share a common factor: a.
2. Factor out the common factor: a(18a^2b – 4b + 10).
3. Focus on factoring the remaining quadratic trinomial: 18a^2b – 4b + 10.
4. Find two numbers whose product is equal to the product of the coefficient of a^2 (which is 18) and the constant term (which is 10). In this case, it is not possible to find such numbers.
Therefore, the factored form of 18a^2b – 4ab + 10a cannot be further simplified.

To factor polynomials completely, we need to find the factors of the quadratic expression that multiply to give the original expression.

Let's solve each of these polynomials step by step:

1. To factor x^2 + 7x + 12 completely:
We need to find two numbers whose sum is 7 and whose product is 12. These numbers are 3 and 4, since 3 + 4 = 7 and 3 * 4 = 12.
So, we factor the polynomial as (x + 3)(x + 4).

2. To factor x^2 - 4 completely:
This is a special case, the difference of squares. It can be factored as (x + 2)(x - 2). The difference of squares formula is a^2 - b^2 = (a + b)(a - b).

3. To factor 18a^2b - 4ab + 10a completely:
Notice that each term has a common factor of 2a. Taking out this common factor, we get:
2a(9ab - 2b + 5).
This is fully factored since we cannot simplify any further.

So, the factored forms of the given polynomials are:
x^2 + 7x + 12 = (x + 3)(x + 4)
x^2 - 4 = (x + 2)(x - 2)
18a^2b - 4ab + 10a = 2a(9ab - 2b + 5).