.jpeg "(5x-25)")
Factoring the Expression (5x - 25)
The expression (5x - 25) is a linear expression, meaning it has a highest power of 1 for the variable 'x'. We can factor this expression by finding the greatest common factor (GCF) of the terms 5x and -25.
Finding the Greatest Common Factor (GCF)
The GCF of 5x and -25 is 5. This is because both 5x and -25 are divisible by 5.
Factoring the Expression
To factor the expression, we can write it as the product of the GCF and the remaining expression after dividing each term by the GCF:
- 5x / 5 = x
- -25 / 5 = -5
Therefore, the factored form of (5x - 25) is:
(5x - 25) = 5(x - 5)
Checking the Factored Expression
We can check if our factorization is correct by expanding the factored expression:
5(x - 5) = 5 * x - 5 * 5 = 5x - 25
This confirms that our factorization is correct.
Conclusion
The expression (5x - 25) can be factored into 5(x - 5) by finding the greatest common factor of the terms and then dividing each term by the GCF. This process allows us to represent the expression in a simpler and more compact form.