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

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

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

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

$latex \displaystyle p={{9}^{n}}$ ——(1)

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

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

$latex \displaystyle 1-p=-80$

$latex \displaystyle p=81$

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

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

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

$latex \displaystyle n=2$

Additional Math (Amath) Secondary 1 and 2 Math, Small Group Math Tuition. Woodlands, Yew Tee, Choa Chu Kang, Admiralty, Sembawang, Yishun and Johor Bahru (JB) Malaysia