when $\displaystyle {{x}^{{2n}}}-p$ is exactly divisible by (x+3), it means that  when you substitute x = -3 into the the expression it equals to zero.

$\displaystyle {{(-3)}^{{2n}}}-p=0$

You will get an equation of p in term of n, name this equation (1)

$\displaystyle {{9}^{n}}-p=0$

$\displaystyle p={{9}^{n}}$ ——(1)

when x=-1 is substituted into the expression $\displaystyle {{x}^{{2n}}}-p$ it will give a remainder of -80 .

$\displaystyle {{(-1)}^{{2n}}}-p=-80$ .

$\displaystyle 1-p=-80$

$\displaystyle p=81$

Substitute p = 81 into equation (1) to find the value of n.

$\displaystyle {{9}^{n}}=81$

$\displaystyle {{9}^{n}}={{9}^{2}}$

$\displaystyle n=2$

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