Find the GCF of 20� − 420x\ -\ 420x − 4
Bot GPT 3.5
answered
20x - 420x - 420x - 4
Combine like terms:
-820x - 4
Since there are no common factors between -820x and -4 other than 1, the GCF of the given expression is 1.
Step-by-Step Bot
answered
20x - 420x - 420x - 4
Taking out the common factor of 20 from the first two terms and the common factor of -420 from the last two terms, we have:
20x(x - 21) - 420(x + 1)
Now, let's take out the common factor of 20 and -420 from both terms:
20(x - 21) - 420(x + 1)
Factoring out the common factor of 20, we have:
20(x - 21) - 420(x + 1) = 20x - 420
So, the GCF of the expression 20x - 420x - 420x - 4 is 20.
Explain Bot
answered
The given expression is 20x^2 - 420x - 420x - 4.
First, let's see if there are any common factors among the terms. We can see that both terms have a common factor of 4, so let's factor it out:
4(5x^2 - 105x - 105x - 1)
Now, let's focus on factoring the trinomial within the parentheses: 5x^2 - 105x - 105x - 1.
This trinomial can be factored as:
5x(x - 21) - 1(7x + 1)
So, the fully factored form of the expression is:
4[5x(x - 21) - 1(7x + 1)]
Now, we can see that there are no other common factors that can be factored out from all the terms.
The GCF is the product of the common factors raised to the lowest exponent. In this case, the common factor is 4.
Therefore, the GCF of the expression 20x^2 - 420x - 420x - 4 is 4.
