Respuesta :
The remainder when f(x) is divided by (x - 3) is 8 and this can be determined by using the factorization method.
Given :
[tex]\rm f(x) = x^4-5x^2-6x-10[/tex]
The following steps can be used in order to determine the remainder if f(x) is divided by (x - 3):
Step 1 - Write the mathematical expression of the statement "f(x) is divided by (x - 3)".
[tex]=\dfrac{x^4-5x^2-6x-10}{x-3}[/tex]
Step 2 - Now, try to factorize the numerator in the above expression.
[tex]=\dfrac{x^4-3x^3+3x^3-9x^2+4x^2-12x+6x-18+18-10}{x-3}[/tex]
Step 3 - Further simplify the above expression.
[tex]=\dfrac{x^3(x-3)+3x^2(x-3)+4x(x-3)+6(x-3)+8}{x-3}[/tex]
[tex]=(x^3+3x^2+4x+6) +\dfrac{8}{x-3}[/tex]
So, the remainder when f(x) is divided by (x - 3) is 8.
For more information, refer to the link given below:
https://brainly.com/question/6810544
