book Maths Puzzle Numerical Ability

the square of a number decreased by the square of one half the number is 108. find the number.

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book Other Question

use synthetic division to divide the following polynomials:
1) divide 3x^5+13x^4+12x-1 by x+5
2) divide 3x^3-8x^2-20x by x+5
No matter how I try, I am not understanding this type of problem....
3x -2y + 5z
____________
2y -3x -5z

This is how I try....
3x (3x-2y + 5z) -(2y + 5z)
_________