Factor completely -5×2 + 10x - 25.
-5(x^2 - 2x + 5)
To factor the expression -5x^2 + 10x - 25 completely, follow these steps:
Step 1: Find the greatest common factor (GCF) of the three terms. In this case, the GCF is 5.
Step 2: Divide each term by the GCF, which is 5. This gives us (-5x^2/5) + (10x/5) - (25/5), which simplifies to -x^2 + 2x - 5.
Step 3: Group the first two terms and the last two terms. This gives us (-x^2 + 2x) - 5.
Step 4: Factor out the GCF from each group. For (-x^2 + 2x), the GCF is x, so we can rewrite it as x(-x + 2).
Step 5: Factor out the negative sign from (-1), so we have -1(x - 2).
Step 6: Combine the two factored terms. This gives us x(-x + 2) - 1(x - 2).
Step 7: Factor out the common binomial (x - 2). This yields (x - 2)(-x + 1).
Therefore, the completely factored form of -5x^2 + 10x - 25 is (x - 2)(-x + 1).