Question

If (px+q)^2=9x^2+kx+16 what is the value of k?

Answer 1

We know that, for a quadratic expression to be monomially-factorable, we have:
\[
(ax+b)^2=a^2x^2+2abx+b^2
\]So, therefore, since we wish to find \(2ab\) in terms of \(a^2\) and \(b^2\):
\[
2ab=2\sqrt{a^2b^2}
\]With this, we solve:
\[
k=2ab=2\sqrt{9\cdot16}=2\cdot3\cdot4=24=k
\]Et voilá.