The solution to the division of the given polynomial expression is:
k = (x+3)(x-4)
Division of polynomials
The division of the given polynomial can be determined by using the rational root theorem which is a method that is popularly used in determining the solutions to a polynomial equation.
From the information given:
[tex]\mathbf{\dfrac{x^3 -3x^2 - 10x +24}{x-2}}[/tex]
Using the rational root theorem;
[tex]\mathbf{\dfrac{(x-2) \dfrac{x^3 -3x^2 - 10x +24}{x-2} }{x-2}}[/tex]
[tex]\mathbf{\dfrac{(x-2)(x^2 -x-12)}{x-2} }}[/tex]
Factor: x² - x - 12
[tex]\mathbf{\dfrac{(x-2)(x+3)(x-4)}{x-2} }}[/tex]
Cancel out the common factor (x-2)
[tex]\mathbf{=(x+3)(x-4) }}[/tex]
Learn more about the division of polynomials here:
https://brainly.com/question/24662212
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