Question

P(x) =2x3 -11x2 -4x +1 g(x) =2x +1

Answer 1

see explanation

Explanation:

If (2x + 1) is a factor then x = -
`(1)/(2)` is a root and P(-
`(1)/(2)` ) = 0 ← Factor theorem

P(-
`(1)/(2)` )

= 2(-
`(1)/(2)` )³ - 11(-
`(1)/(2)` )² - 4(-
`(1)/(2)` ) + 1

= -
`(1)/(4)` -
`(11)/(4)` + 2 + 1

= -
`(12)/(4)` + 3

= - 3 + 3

= 0

Since P(-
`(1)/(2)` ) = 0 then g(x) is a factor of P(x)