Question

question 10 of 10
find the roots of the polynomial shown. what is the value of the largest root?
$f(x) = 3x^3 + 12x^2 + 3x - 18$
answer here

Explanation:

Step1: Factor out common term

$f(x)=3(x^3 + 4x^2 + x - 6)$

Step2: Find rational root

Test $x=1$: $1+4+1-6=0$, so $(x-1)$ is factor.

Step3: Polynomial division

Divide $x^3+4x^2+x-6$ by $(x-1)$: $x^2+5x+6$

Step4: Factor quadratic

$x^2+5x+6=(x+2)(x+3)$

Step5: List all roots

$x=1, x=-2, x=-3$

Step6: Identify largest root

Largest root is $1$.

Answer:

1