Question

find all zeros of $f(x) = x^3 + 2x^2 + x + 2$. enter the zeros separated by commas.
question help: video 1 video 2 read 1 written example 1

Explanation:

Step1: Group terms for factoring

$f(x) = (x^3 + 2x^2) + (x + 2)$

Step2: Factor out common terms

$f(x) = x^2(x + 2) + 1(x + 2)$

Step3: Factor out $(x+2)$

$f(x) = (x^2 + 1)(x + 2)$

Step4: Solve $x+2=0$

$x + 2 = 0 \implies x = -2$

Step5: Solve $x^2+1=0$

$x^2 = -1 \implies x = \pm i$

Answer:

$-2, i, -i$