Question

Which polynomial represents a perfect square polynomial? Select all that apply.

1.x^2+8x+16

2.4x^2+10x+25

3.9x^2+48x+64

4.16x^2+4x+1

Answer 1

well lets try to perfect square each one .... A quadratic equation has the following form
\(ax^2+bx+c\) and when we perfect square it we have \((ax+\sqrt{c})^2\) and \(b=2*a*\sqrt{c}\)


\[x^2+8x+16\]
So a in this case a=1 and c=16 and\(\sqrt{16}=4\) and b=8

\[(x+4)^2\]

Lets see if \( b=2*a*\sqrt{c}\) so \( 2*1*4=2*4=8\)
So the first option is a perfect square