Question

$x^3 - 3x^2 - 40x + 84$ select your answer below the calculator options: $x = -7, 2, 6$; $x = -2, 6, 7$; $x = -1, 6, 7$; $x = -6, 2, 7$

Explanation:

Step1: Use Rational Root Theorem

Possible rational roots: $\pm1, \pm2, \pm3, \pm4, \pm6, \pm7, \pm12, \pm14, \pm21, \pm28, \pm42, \pm84$

Step2: Test $x=2$ in polynomial

$2^3 - 3(2)^2 -40(2)+84 = 8 - 12 -80 +84 = 0$

Step3: Factor out $(x-2)$

Use polynomial division: $\frac{x^3-3x^2-40x+84}{x-2}=x^2 -x -42$

Step4: Factor quadratic

$x^2 -x -42=(x-7)(x+6)$

Step5: Find all roots

Set each factor to 0: $x-2=0$, $x-7=0$, $x+6=0$

Answer:

$x=-6, 2, 7$ (Option: $x=-6, 2, 7$)