Answer:
( 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
