Factor this expression completely.
35x−40 (1 point)
7(5x+8)
7(5x−8)
5(7x+8)
5(7x−8)
The correct answer is:
7(5x - 8)
To factor the expression 35x - 40 completely, we can start by finding the greatest common factor (GCF) of the coefficients.
The GCF of 35 and 40 is 5.
Next, we divide each term in the expression by the GCF, which is 5:
35x ÷ 5 = 7x
-40 ÷ 5 = -8
Therefore, the factored form of the expression is:
5(7x - 8)
So, the correct answer is 5(7x - 8).
To factor the expression 35x - 40 completely, we need to find the greatest common factor (GCF) of the terms and then divide each term by this factor.
First, let's find the GCF of the two terms: 35x and -40.
The prime factorization of 35x is 5 * 7 * x.
The prime factorization of -40 is -1 * 2^3 * 5.
The GCF is the product of the common prime factors, raised to the lowest power they appear in both terms. In this case, the common prime factor is 5, so the GCF is 5.
Now, divide each term by the GCF (5):
35x ÷ 5 = 7x
-40 ÷ 5 = -8
Therefore, the completely factored expression is:
5(7x - 8)
So, the correct answer is "5(7x - 8)."