Question

The value of p for which x3+4x-px+8 is divisible by x-2 is

Answer 1

Answer :


As given that

$g(x) = {x}^{3} + 4x - px + 8 \: \: is \: divisible \: by \: \: (x - 2)$


So firstly find the zero or root of x - 2

=> Zero of x - 2 =

=> x - 2 = 0

=> x = 0 + 2

=> x = 2

So, Zero of x - 2 is 2.


Now, if x - 2 is divisible by p(x)

Then,

g(2) = 0


So, To find the value of p put 2 at the place of x in the given polynomial.


Therefore ---


$g(2) = {2}^{3} + 4(2) - p(2) + 8 = 0 \\ \\ = > 8 + 8 - 2p + 8 = 0 \\ \\ = > 16 - 2p + 8 = 0 \\ \\ = > 24 - 2p = 0 \\ \\ = > - 2p = 0 - 24 \\ \\ = > - 2p = - 24 \\ \\ = > p = \frac{ - 24}{ - 2} \\ \\ = > p = \frac{24}{2} \\ \\ = > p = 12 \\ \\ verification \: - - \\ \\ put \: \: p = 12 \: \: in \: g(2) \\ \\ {2}^{3} + 4(2) - 12(2) + 8 = 0 \\ \\ = > 8 + 8 - 24 + 8 = 0 \\ \\ = > 24 - 24 = 0 \\ \\ = > 0 = 0 \\ \\ \: l.h.s \: = \: r.h.s \\ \\ so \: \: the \: \: value \: \: of \: \: p \: \: is \: \: true$



HOPE IT WOULD HELP YOU