Question

. please please solve this answer in detail please do this it is very urgent to me​

Answer 1

Answer:

Hey mates here is your ans

Answer 2

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Let

$f(x) = {x}^{3} - 5 {x}^{2} - px + 24$

$g(x) = x - 4$

So

Now it is given that

${x}^{3} - 5 {x}^{2} - px + 24 = (x - 4) \: q(x)$

So (x - 4) is a factor of ${x}^{3} - 5 {x}^{2} - px + 24$

So Remainder = 0

Now for the zero of polynomial g(x) we have

$g(x) = 0$

$\implies \: x - 4 = 0$

$\implies \: x \: = 4$

So By the Remainder Theorem the Remainder is

$= f(4)$

$= {4}^{3} - 5 \times {4}^{2} - p \times 4 + 24$

$= 64 - 80 - 4p + 24$

$= 8 - 4p$

By the given condition

$8 - 4p = 0$

$\implies \: 4p = 8$

$\therefore \: p \: = 2$

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