Answer:
The correct option will be B.
[tex]3 {x}^{2} + 4x - 6[/tex]
.
Step-by-step explanation:
The given polynomial is
[tex]3 {x}^{3} – 11 {x}^{2} – 26x + 30[/tex]
It is required to find the quotient when the given polynomial is divided by x-5.
The given polynomial can be written as,
[tex]3 {x}^{3} – 11 {x}^{2} – 26x + 30 = 3 {x}^{2} (x - 5) + 4x(x - 5) - 6(x - 5) \\ 3 {x}^{3} – 11 {x}^{2} – 26x + 30 =(3 {x}^{2} - + 4x - 6)(x - 5)[/tex]
Now, by dividing the given polynomial by x-5, the quotient will be,
[tex]3 {x}^{2} + 4x - 6[/tex]
Therefore, the option B
[tex]3 {x}^{2} + 4x - 6[/tex]
will be correct.
For more details, refer the link:
https://brainly.com/question/12520197?referrer=searchResults
