Answer:
(x−5)(5(x−1))
Explanation:
To factor the quadratic expression
5
�
2
−
30
�
+
25
5x
2
−30x+25, we first check if it can be factored using the standard quadratic factoring method, which involves finding two numbers that multiply to the product of the leading coefficient (5) and the constant term (25), and add up to the middle coefficient (-30).
The product of 5 and 25 is
5
×
25
=
125
5×25=125. The possible pairs of numbers that multiply to 125 are:
1 × 125
5 × 25
Among these pairs, the pair that adds up to -30 is 5 and -25.
So, we can rewrite the expression as:
5
�
2
−
25
�
−
5
�
+
25
5x
2
−25x−5x+25
Now, we group the terms:
5
�
(
�
−
5
)
−
5
(
�
−
5
)
5x(x−5)−5(x−5)
Now, we can factor out the common factor
�
−
5
x−5:
(
�
−
5
)
(
5
�
−
5
)
(x−5)(5x−5)
Finally, we notice that
5
�
−
5
5x−5 can be further simplified by factoring out a common factor of 5:
(
�
−
5
)
(
5
(
�
−
1
)
)
(x−5)(5(x−1))
So, the factored form of the expression
5
�
2
−
30
�
+
25
5x
2
−30x+25 is
(
�
−
5
)
(
5
�
−
5
)
(x−5)(5x−5), or alternatively
(
�
−
5
)
(
5
(
�
−
1
)
)
(x−5)(5(x−1)).
