Question

The sum of all possible values of n where n is an integer when 4n2 + 6n +8 is divided by 2n gives an integer , is
a.2
b.6
c.0
d.7

Answer 1

The value of p is 16

Solution:

Given the polynomial f(x)= x^3+4x^2-px+8f(x)=x3+4x2−px+8

For f(x) to be exactly divisible by 2, we must have f(2)=0f(2)=0 by remainder and factor theorem

Since given that, (x – 2) is exactly divisible by 2.

Thus, x = 2

$Substituting x=2 in the given expression, we get,</p><p> \begin{lgathered}\begin{aligned} f ( 2 ) = & 2 ^ { 3 } + 4 \times 2 ^ { 2 } - 2 p + 8 = 0 \\\\ & 8 + 16 - 2 p + 8 = 0 \\\\ & 16 + 16 - 2 p = 0 \end{aligned}\end{lgathered} </p><p> \begin{lgathered}\begin{array} { c } { 32 - 2 p = 0 } \\\\ { 2 p = 32 } \\\\ { p = 16 } \end{array}\end{lgathered} </p><p>Which gives p=16  </p><p>Thus, the value of p will be 16.$

Answer 2

Answer:

.

Step-by-step explanation:

answer is 16..................