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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