factor 2x^2-50 completely
2x^2-50
common factor, followed by difference of squares:
= 2(x^2 - 25)
= 2(x-5)(x+5)
To factor the expression 2x^2 - 50, first, look for the greatest common factor (GCF) of the terms.
The GCF of 2 and -50 is 2.
Now, factor out the GCF from the expression:
2(x^2 - 25)
Next, notice that the remaining expression, x^2 - 25, can be further factored using the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b).
In this case, a = x and b = 5. So, apply the difference of squares formula to factor x^2 - 25:
(x + 5)(x - 5)
Therefore, the fully factored form of 2x^2 - 50 is:
2(x + 5)(x - 5)
To factor the quadratic expression 2x^2 - 50 completely, follow these steps:
Step 1: Identify the greatest common factor (GCF) if possible. In this case, both terms have a common factor of 2, so factor it out:
2(x^2 - 25).
Step 2: Recognize that x^2 - 25 is a difference of squares, which can be factored as (x + 5)(x - 5). Thus, we have:
2(x + 5)(x - 5).
Therefore, the completely factored form of 2x^2 - 50 is 2(x + 5)(x - 5).