Question

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

Answer 1

Answer:

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

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

Step-by-step explanation:

Given the function

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

Use the rational root theorem.

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

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

$\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:11,\:22}{1}$

$-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2$

$=\left(x+2\right)\frac{x^3-4x^2-x+22}{x+2}$

as

$\frac{x^3-4x^2-x+22}{x+2}=x^2-6x+11$        ∵ $x^3-4x^2-x+22=\left(x+2\right)\left(x^2-6x+11\right)$

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:

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