What are the factors of the polynomial function? Use the rational root theorem to determine the factors. f (x) = 2x³ + x² - 8x - 4.

(x + 2) (x - 2) (2x + 1)

Step-by-step explanation:

coefficient of x³ is 2 and denote it with q and denote - 4 as p

the set of possible rational roots through rational theorem will be within ± (p/q)

now factors of - 4 are ± (1,2,4) and factors of 2 are ± (1,2) the possible rational roots are ± (1/1, 1/2, 2/1, 2/2, 4/1, 4/2) which reduces to ± (1, 1/2, 2, 4)

substitute each of the value into the equation

f (x) = 2x³ + x² - 8x - 4 to the root (that gives f (x) = 0)

the equation can be made easy writing it in reduced form

2x³ + x² - 8x - 4

(2x³ + x²) - (8x + 4)

x² (2x + 1) - 4 (2x + 1)

(x² - 4) (2x + 1)

(x + 2) (x - 2) (2x + 1) are the factors which correspond to 2, - 2, - 1/2 roots