Question

if
x + p is a factor of p(x) = x⁵-p²x³+2x+p+1 find the value of p​

Answer 1

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Answer 2

Given:-

• f(x) = x + p

• P(x) = $\rm{x^5 - p^2x^3 + 2x + p + 1}$

To Find:-

• The Value of p

Now,

$\implies\rm{ f(x) = x + p = 0}$

$\implies\rm{ x = -p}$

Now Putting the value of f(x) in P(x)

$\implies\sf{ p(x) = x^5 - p^2x^3 + 2x + p + 1}$

$\implies\sf{ (-p)^5 -(-p)^2(-p)^3 + 2(-p) + p + 1 = 0}$

$\implies\sf{ -p^5 + p^5 -2p + p + 1 = 0}$

$\implies\sf{\cancel{-p^5 + p^5}-2p + p + 1 = 0}$

$\implies\sf{ -2p + p + 1 = 0}$

$\implies\sf{ -p = -1}$

$\implies\sf{ p = 1}$.

Thus, The Value of p is 1.