Find the value of c

Question

If p(x) =2x³+cx²-5x-6 and x-2 is a factor of p(x)

 

Answer 1

The function

p(x)  =  2x³ + cx² - 5x - 6

if x - 2 is a factor of p(x) then p(2) = 0.

Substitute x = 2 in p(x)

p(2)  =  2(2)³ + c(2)² - 5(2) - 6

0  =  2(8) + c(4) - 10 - 6                             [ Since p(2) = 0]

0  =  16 + 4c - 16

0  =  4c

c  = 0

Answer :

The value c  = 0