factor this expression completley
35x-40
To factor the expression 35x - 40 completely, we can begin by finding the greatest common factor (GCF) of the given terms: 35 and 40. The GCF of 35 and 40 is 5.
Now, we can factor out the GCF from each term:
35x - 40 = 5(7x - 8)
Therefore, the expression 35x - 40 is completely factored as 5(7x - 8).
To factor the expression 35x - 40 completely, let's first look for any common factors between the two terms:
The greatest common factor (GCF) between 35 and 40 is 5.
Next, we rewrite the expression by factoring out the GCF (which is 5):
5(7x - 8)
Now, to further factor the expression inside the parentheses (7x - 8), we look for factors of the constant term (-8) that add up to the coefficient of the x term (7).
Although there are no obvious factors that add up to 7 and multiply to -8, we can still factor it by considering the middle term as a sum of two terms:
7x can be expressed as (x)(7) or (7)(x).
-8 can be expressed as (-1)(8) or (1)(-8).
Let's try factoring it as (x + a)(7x + b):
(x + a)(7x + b) = 7x^2 + (7a + b)x + ab
In order to get the 7a + b term to equal 7x, we can assign a = -1 and b = -1:
(x - 1)(7x - 1)
Therefore, the expression 35x - 40 can be factored completely as:
5(x - 1)(7x - 1)
To factor the expression completely, you need to look for common factors in each term and then factor them out.
Let's start with the expression 35x - 40.
Step 1: Find the greatest common factor (GCF) of the coefficients (35 and 40) and the variable (x).
The GCF of 35 and 40 is 5, and both terms have a variable x.
Step 2: Divide each term by the GCF and factor it out.
35x divided by 5x is 7, and -40 divided by 5 is -8.
So, the factored expression is 5(7x - 8).
This means that the original expression 35x - 40 can be completely factored as 5(7x - 8).