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

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

mimi_x3 · Answer

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