Question

Factor −5x2 + 10x.

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Answer 1

C. 5x(-x + 2)

Explanation:

To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.

Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.

Both terms have the common factor of 5x, so we can factor out 5x:

5x(-x + 2)

Therefore, the factored form of -5x² + 10x is -5x(x - 2).

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Additional notes:

If we expand the expressions in the given answer options, we get:

A. −5x(x + 2) = -5x² - 10x

B. 5(−x² + 10x) = -5x² + 50x

C. 5x(−x + 2) = -5x² + 10x

D. x(5x + 10) = 5x² + 10x

Hence confirming that the correct answer is option C.

Answer 2

To factor
`-5x^2+10x`, we can begin by factoring out the greatest common factor, which is
`-5x`:

• 
  `-5x^2 + 10x = \boxed{-5x(x - 2)}`

We can check our answer by distributing
`-5x` to the expression inside the parentheses:

• 
  `\begin{aligned}-5x(x - 2)& = (-5x)(x) + (-5x)(-2)\\& = -5x^2 + 10x\end{aligned}`

`\therefore` The answer is
`-5x(x-2)`.

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