Answer: (x - 2)(x + 2)(2x + 1)
Step-by-step explanation:
q p
f(x) = 2x³ + x² - 8x - 4
rational root theorem: [tex]\frac{p}{q} = +/- \frac{1, 2, 4}{1, 2}[/tex] so the possible roots are: +/- 1, 2, 4, [tex]\frac{1}{2}[/tex]
Let's try x = 2
2 | 2 1 -8 -4
| ↓ 4 10 4
2 5 2 0 remainder is 0 so (x - 2) is a factor
0 = (x - 2) (2x² + 5x + 2)
0 = (x - 2) (x + 2)(2x + 1)
