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].
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].
