Question

Factor completely −5x² + 10x − 25.

a. −5(x² − 2x + 5)
b. −1(x² − 10x + 25)
c. −5x(x² − 2x + 5)
d. −5(x² + 2x − 5)

Answer 1

To factor the quadratic polynomial -5x² + 10x - 25 completely, we start by factoring out a common factor of -5 and then attempt to factor the quadratic expression inside the parentheses.

Step-by-step explanation:

To factor the quadratic polynomial -5x² + 10x - 25 completely, we need to find two binomials that, when multiplied, give us the original polynomial. We can start by factoring out a common factor of -5:

-5x² + 10x - 25 = -5(x² - 2x + 5)

Next, we can attempt to factor the quadratic expression inside the parentheses. However, since it does not factor further, the factored form of the polynomial is:

-5(x² - 2x + 5)

Therefore, option a. -5(x² - 2x + 5) is the correct answer.