Answer:
The value of p is 16
Solution:
Given the polynomial [tex]f(x)= x^3+4x^2-px+8[/tex]
For f(x) to be exactly divisible by 2, we must have [tex]f(2)=0[/tex] by remainder and factor theorem
Since given that, (x – 2) is exactly divisible by 2.
Thus, x = 2
Substituting x=2 in the given expression, we get,
[tex]\begin{aligned} f ( 2 ) = & 2 ^ { 3 } + 4 \times 2 ^ { 2 } - 2 p + 8 = 0 \\\\ & 8 + 16 - 2 p + 8 = 0 \\\\ & 16 + 16 - 2 p = 0 \end{aligned}[/tex]
[tex]\begin{array} { c } { 32 - 2 p = 0 } \\\\ { 2 p = 32 } \\\\ { p = 16 } \end{array}[/tex]
Which gives p=16
Thus, the value of p will be 16.
