how do u factor these polynomials~

5x^2 - 5x-60

81-x^4

18a^2b-50b

(5x-20)(x+3)

-(x^2-9)(x^2+9)

Then are you sure the third one is written right? 18a^2b- is a to the 2b or is b something else

its A squared b

To factor polynomials, we need to look for common factors and apply techniques like factoring by grouping or using special factoring formulas if applicable. Let's go through each polynomial one by one:

1. 5x^2 - 5x - 60:
First, check if there is a common factor among the coefficients:

The coefficients 5, -5, and -60 have a common factor of 5, so we can factor it out:
5(x^2 - x - 12)

Now, let's focus on factoring the quadratic expression inside the parentheses:
(x^2 - x - 12)

To further factor this quadratic expression, we need to find two numbers whose product is -12 and whose sum is -1 (coefficient of x). The numbers -4 and 3 satisfy these conditions, so we can write the quadratic expression as:
(x - 4)(x + 3)

Therefore, the factored form of 5x^2 - 5x - 60 is:
5(x - 4)(x + 3)

2. 81 - x^4:
Notice that this expression has the form of a difference of squares (a^2 - b^2). The square of 9 is 81, and the square of x^2 is x^4, so we can write the expression as:
(9)^2 - (x^2)^2

Using the difference of squares formula: a^2 - b^2 = (a + b)(a - b), we can factor it as:
(9 + x^2)(9 - x^2)

The second factor is also a difference of squares (9^2 - x^2), which can be further factored as (9 + x)(9 - x).

Thus, the factored form of 81 - x^4 is:
(9 + x^2)(9 + x)(9 - x)

3. 18a^2b - 50b:
In this polynomial, we can factor out the common factor 'b':
b(18a^2 - 50)

Now, let's focus on factoring the quadratic expression inside the parentheses: 18a^2 - 50

We can look for a common factor among the coefficients, and in this case, they are both even numbers. Let's factor out 2:
2(9a^2 - 25)

This quadratic expression is a difference of squares (3a)^2 - 5^2, so we can further factor it as:
2(3a + 5)(3a - 5)

Thus, the factored form of 18a^2b - 50b is:
b(3a + 5)(3a - 5)

By following these steps and applying the appropriate factoring techniques, you can factor different types of polynomials.