Factorize 3x³ - 3x² - 90x Give an explanation of 3x(x² - x - 30)?

To factorize 3x³ - 3x² - 90x, we can first factor out the common factor of 3x:

3x(x² - x - 30)

Now, we need to factorize the quadratic expression inside the parentheses, x² - x - 30. This can be factored into two binomial factors:

(x + 5)(x - 6)

Therefore, the factorization of 3x³ - 3x² - 90x is:

3x(x + 5)(x - 6)

Explanation of 3x(x² - x - 30):

- We first factor out the common factor of 3x from the given expression.
- Then, we factorize the quadratic expression x² - x - 30 into two binomial factors, (x + 5)(x - 6).
- Finally, we combine the common factor and the factored quadratic expression to get the final factorization of 3x³ - 3x² - 90x as 3x(x + 5)(x - 6).

Factorization of 3x³ - 3x² - 90x

1. Factor out the greatest common factor (GCF) of the terms: 3x
3x³ - 3x² - 90x = 3x(x² - x - 30)

2. Factor the quadratic expression x² - x - 30 as follows:
- Find two numbers that sum to -1 and multiply to -30: -6 and 5
- Rewrite the middle term as the sum of these numbers: 3x(-6x + 5)
- Factor by grouping: 3x(-6x + 5) = 3x(-x - 6)(x - 5)

Explanation of 3x(x² - x - 30)

3x is the GCF of the terms x³, x², and 90x. We can factor it out as a common factor from each term.

x² - x - 30 is a quadratic expression that can be factored by finding two numbers that sum to the coefficient of the middle term (-1) and multiply to the constant term (-30). These numbers are -6 and 5.

Therefore, we can factor 3x(x² - x - 30) as 3x(-x - 6)(x - 5).