Answer:
The expression that have the following quotient is:
- [tex]\dfrac{-4x^2+20x-25}{-2x+5}[/tex]
- [tex]\dfrac{-14x^2+35x}{-7x}[/tex]
- [tex]\dfrac{12x^2-58x+70}{6x-14}[/tex]
Step-by-step explanation:
1)
[tex]\dfrac{-4x^2+20x-25}{-2x+5}[/tex]
It could also be written as:
[tex]\dfrac{-(5-2x)^2}{5-2x}\\\\\\=-(5-2x)\\\\\\=2x-5[/tex]
Hence, we get the quotient:
[tex]2x-5[/tex]
Option: (1) is correct.
2)
[tex]\dfrac{-14x^2+35x}{-7x}[/tex]
which is simplified as follows:
[tex]\dfrac{-7x(2x-5)}{-7x}\\\\\\=2x-5[/tex]
Option: (2) is correct.
3)
[tex]\dfrac{12x^2-58x+70}{6x-14}[/tex]
which is simplified as follows:
[tex]=\dfrac{2(2x-5)(3x-7)}{2(3x-7)}\\\\\\=2x-5[/tex]
Hence, option: (3) is correct.
4)
[tex]\dfrac{6x^2-10x-4}{3x+1}[/tex]
On simplifying:
[tex]\dfrac{2(3x+1)(x-2)}{3x+1}\\\\\\=2(x-2)\\\\\\=2x-4[/tex]
Hence, option: (4) is incorrect.
5)
[tex]\dfrac{18x-45}{9x}[/tex]
on simplifying:
[tex]\dfrac{9(2x-5)}{9x}\\\\\\=\dfrac{2x-5}{x}[/tex]
Hence, option: (4) is incorrect.
