Rewrite the expression [tex]\(25x - 5x^2\)[/tex] using a common factor of the terms.

A. [tex]\(x(25 - x)\)[/tex]
B. [tex]\(5x(20 - x)\)[/tex]
C. [tex]\(5(5 - x)\)[/tex]
D. [tex]\(5x(5 - x)\)[/tex]



Answer :

To rewrite the expression [tex]\(25x - 5x^2\)[/tex] using a common factor of the terms, follow these steps:

1. Identify the common factor:
- Both terms, [tex]\(25x\)[/tex] and [tex]\(-5x^2\)[/tex], share a common factor. Examine the coefficients (25 and -5) and the variable [tex]\(x\)[/tex].
- The greatest common factor of 25 and -5 is 5.
- Both terms include [tex]\(x\)[/tex], so [tex]\(x\)[/tex] is also part of the common factor.

2. Factor out the common factor:
- The common factor is [tex]\(5x\)[/tex].
- Divide each term by [tex]\(5x\)[/tex]:
[tex]\[ \frac{25x}{5x} = 5 \quad \text{and} \quad \frac{-5x^2}{5x} = -x \][/tex]

3. Write the factored form:
- Express the original expression as a product of the common factor and the resulting terms:
[tex]\[ = 5x (5 - x) \][/tex]

The expression [tex]\(25x - 5x^2\)[/tex] can be rewritten as [tex]\(5x(5 - x)\)[/tex].

So, the correct answer is:

D. [tex]\(5x(5 - x)\)[/tex].