Question

PLEASE HELPP‼️‼️ write in factored form g(x)= x^3 - 4x^2 - x + 22

Answer 1

`g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22` in the factored form will be:

• 
  `g\left(x\right)=x^3-4x^2-x+22=\:\left(x+2\right)\left(x^2-6x+11\right)`

Explanation:

Given the function

`g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22`

Use the rational root theorem.

`a_0=22,\:\quad a_n=1`

`\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:11,\:22,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1`

`\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm (1,\:2,\:11,\:22)/(1)`

`-(2)/(1)\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2`

`=\left(x+2\right)(x^3-4x^2-x+22)/(x+2)`

as

`(x^3-4x^2-x+22)/(x+2)=x^2-6x+11` ∵
`x^3-4x^2-x+22=\left(x+2\right)\left(x^2-6x+11\right)`

so the expression becomes

`x^3\:-\:4x^2\:-\:x\:+\:22=\left(x+2\right)\left(x^2-6x+11\right)`

Therefore,

`g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22` in the factored form will be:

• 
  `g\left(x\right)=x^3-4x^2-x+22=\:\left(x+2\right)\left(x^2-6x+11\right)`