Factor completely -5×2 + 10x - 25.
0-5(x2-2x + 5)
0-1(×2 - 10x + 25)
0-5х(×2 - 2x + 5)
O-5(x2 + 2x - 5)
The correct answer is:
-5(x-5)(x+1)
To factor the expression -5x^2 + 10x - 25 completely, you can start by factoring out the greatest common factor, which in this case is -5:
-5(x^2 - 2x + 5)
Now let's focus on factoring the quadratic trinomial inside the parentheses, x^2 - 2x + 5. Since this trinomial cannot be factored using integer values, we will need to use the quadratic formula or complete the square. In this case, we will use the quadratic formula.
x = (-(-2) ± √((-2)^2 - 4(1)(5))) / (2(1))
Simplifying the equation further:
x = (2 ± √(4 - 20)) / 2
x = (2 ± √(-16)) / 2
Since the discriminant is negative, there are no real solutions for x. Therefore, the quadratic trinomial x^2 - 2x + 5 is not factorable using real numbers.
Thus, the factored form of the expression -5x^2 + 10x - 25 is -5(x^2 - 2x + 5).