Factor this expression completely.35x−40
Step 1: Find the greatest common factor (GCF) of the terms 35x and -40.
The GCF of 35 and 40 is 5.
Step 2: Divide each term by the GCF:
35x / 5 = 7x
-40 / 5 = -8
Step 3: Write the expression after factoring out the GCF:
The expression 35x - 40 can be factored as 5(7x - 8).
To factor the expression 35x - 40 completely, you can start by finding the greatest common factor (GCF) of the two terms. In this case, the GCF is 5.
Step 1: Factor out the GCF of 5:
5(7x - 8)
Step 2: The expression is now fully factored.
To factor the expression 35x - 40 completely, we can start by factoring out the greatest common factor (GCF) if there is one. In this case, both terms have a common factor of 5:
35x - 40 = 5(7x - 8)
Next, we can look for further ways to factor the expression. It is a binomial, meaning it has two terms. We can check if it fits any special factoring patterns like a difference of squares or a perfect square trinomial. However, neither of these patterns apply to our expression.
Therefore, we can consider if it is possible to use any simple algebraic techniques to factorize the expression further. In this case, there is no straightforward factorization without introducing irrational numbers or complex numbers. So, the factored form is:
35x - 40 = 5(7x - 8)
It is important to note that not all expressions can be factored completely using rational numbers. Some expressions may require more advanced techniques or may not be factorable at all.