Answer:
[tex]\textsf{C)} \quad 2(3x-5)^2[/tex]
Step-by-step explanation:
Given quadratic:
[tex]18x^2-60x+50[/tex]
Factor out the common term 2:
[tex]\implies 2(9x^2-30x+25)[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
[tex]\implies ac=9 \cdot 25=225[/tex]
[tex]\implies b=-30[/tex]
Therefore, the two numbers are: -15 and -15.
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies 2(9x^2-15x-15x+25)[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 2(3x(3x-5)-5(3x-5))[/tex]
Factor out the common term (3x - 5):
[tex]\implies 2(3x-5)(3x-5)[/tex]
Apply the exponent rule aa=a²:
[tex]\implies 2(3x-5)^2[/tex]