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Use an appropriate procedure to show that x-4 is a factor of the function f(x)=2x^3-5x^2-11x-4. Show work pleassseeee

Respuesta :

f(4)=2(4)^3-5(4)^2-11(4)-4=128-80-44-4=0
Solution is 4

The factors of the given polynomial are [tex](x+1)[/tex] and [tex](2x^{2} -7x -4)[/tex]

What is the factor of polynomial?

If p(x) be the polynomial then q(x) is called its factor if q(x) divides p(x) without leaving any remainder.

How to find the factor of the  cubic polynomial?

If p(x) be a cubic polynomial then the following steps are required to find the factor of polynomial :

  • Find x = a, where p(a) = 0.
  • Then (x - a) is the factor of p(x).
  • Now divide p(x) by (x- a)
  • And then we factorize the quotient by splitting the middle term.

According to the given question.

We have a cubic polynomial

[tex]f(x) = 2x^{3} -5x^{2} -11x - 4[/tex]

Since, at x = -1, we are getting f(x) = 0.

Therefore, (x + 1 ) is the one factor of the given cubic polynomial.

So, when we divide f(x) by (x + 1) we get an another quadratic polynomial

[tex]2x^{2} -7x-4[/tex]

Hence, the factors of the given polynomial are [tex](x+1)[/tex] and [tex](2x^{2} -7x -4)[/tex] .

Find out more information about factors of cubic polynomial here:

https://brainly.com/question/8878887

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