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The expression \(\frac13x^2-2\) can be rewritten as \(\frac13 (x-k)(x+k)\),where k is a positive constant. What is the value of k ?
\(\left(7532+100y^2\right)\;+\;10(10y^2-110)\)
The expression above can be written in the form \(ay^2+b\), where a and b are constants. What is the value of \(a+b\)?
The sum of \(-2x^2+x+31\) and \(3x^2+7x-8\) can be written in the form \(ax^2+bx+c\), where a, b, and c are constants. What is the value of \(a+b+c\)?
The polynomial \(p^4+4p^3+3p^2-4p-4\) can be written as \(\left(p^2-1\right)\left(p+2\right)^2\). What are all of the roots of the polynomial?
If \((ac+2)(bx+7)=15x^2+cx+14\) for all values of x, and \(a+b=8\), what are the two possible values for c ?
If \(9^{3a}=81\) what is the value of a?