Question

Find the value of p if 2x-1 is the factor of 2x³+px²+11x+p+3

Answer 1

p(x) = 2x³ +px² +11x +p+3

Given that (2x-1) is a factor.

2x-1 = 0

x = 1/2

As 2x-1 is a factor of p(x), we get,

p(1/2) = 2(1/2)³ +p(1/2)² +11(1/2) + p +3

= 2(1/8) +p(1/4) +11/2 +p +3

= 1/4 + p/4 +11/2 +p +3

= (1+ p+22 +4p +12) /4

= (35 +5p )/4

As 2x-1 is a factor, the remainder would be zero,

(35 +5p)/4 =0

35 +5p =0

5p =-35

p =-35/5 =-7

p = -7

Therefore, the value of p is -7.