Question 1127752


{{{ f(x) = x^4 + 5x^3 - x^2 - 5x }}}

Select EACH correct answer.

A. {{{f(x)}}} divided by {{{(x + 5)}}} has a remainder of {{{0}}}.

factor {{{ f(x)}}}:

{{{ f(x) = x^4 + 5x^3 - x^2 - 5x }}}

{{{ f(x) = (x^3 + 5x^2 - x - 5)x }}}

{{{ f(x) = x((x^3 + 5x^2) - (x + 5)) }}}

{{{ f(x) = x(x^2(x + 5) - (x + 5)) }}}

{{{ f(x) = x(x^2 -1) (x + 5) }}}

{{{ f(x) = (x^3 -x) (x + 5) }}}

so,

{{{x^4 + 5x^3 - x^2 - 5x = (x^3 - x) * (x + 5) + 0}}} -> {{{A}}} is correct


B. {{{(x - 5) is a factor of {{{f(x)}}}-> {{{NOT}}} correct


C. {{{f(5)= 0}}}-> {{{NOT}}} correct
{{{ f(x) = 5^4 + 5*5^3 - 5^2 - 5*5 =1200}}}


D. {{{f(x)= 0}}} when {{{x = -5}}}.->correct

use factored form:
{{{ 0 = (x^3 -x) (x + 5) }}}
{{{ 0 = (x + 5)  }}}=>{{{x=-5}}}


so, you need to choose all correct answers and they are:

A. {{{f(x)}}} divided by {{{(x + 5)}}} has a remainder of {{{0}}}.
D. {{{f(x)= 0}}} when {{{x = -5}}}.