Question

find a value for c so that the polynomial y^2 + 10y + c factors to (y+5)^2

Answer 1

Notice that

$\begin{gathered} (y+5)^2=y^2+10y+25 \\ \text{and} \\ y^2+10y+c=(y+5)^2 \\ \Rightarrow y^2+10y+c=y^2+10y+25 \\ \Rightarrow c=25 \end{gathered}$

Then, the answer is c=25.