Question

value of 'p' for which (x^2+3x+p) divisible by (x-2)is

Answer 1

Answer:

$\red { Value \: of \: p } \green {= -10}$

Step-by-step explanation:

$Let \:p(x) = x^{2}+3x+p$

$If \: p(x) \:is \: divisible \: (x-2) \:then \: the \\remainder \: p(2) = 0$

/*

Factor theorem :

If (x-a) is a factor of the polyomial p(x), then

p(a) = 0 . */

$p(2) = 0$

$\implies 2^{2} + 3\times 2 + p = 0$

$\implies 4 + 6 + p = 0$

$\implies 10 + p = 0$

$\implies p = -10$

Therefore.,

$\red { Value \: of \: p } \green {= -10}$

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Answer 2

It is divisible by - 10 hence , Value of p = - 10