factor by grouping x^3-5x^2+5x-25
(x^3 + 5 x) - (5x^2+25)
x(x^2+5) - 5(x^2+5)
(x-5)(x^2+5)
To factor the expression x^3 - 5x^2 + 5x - 25 by grouping, follow these steps:
Step 1: Group the terms into pairs
In this case, we can group the first two terms (x^3 - 5x^2) as well as the last two terms (5x - 25).
(x^3 - 5x^2) + (5x - 25)
Step 2: Factor out the greatest common factor from each pair
From the first pair, we can factor out x^2, and from the second pair, we can factor out 5.
x^2(x - 5) + 5(x - 5)
Step 3: Observe the common factor
Notice that both terms now have a common factor of (x - 5).
(x^2 + 5)(x - 5)
Therefore, the factored form of x^3 - 5x^2 + 5x - 25 is (x^2 + 5)(x - 5).