SOLUTION
The expression is given as
[tex]u^2+20u+n[/tex]
The value of n makes the expression a perfect square trinomial.
To find the value of n, we have
Identify the coefficient of u and divide by 2
[tex]\begin{gathered} \text{the coefficient of u=20} \\ \text{divide by 2=}\frac{\text{20}}{2}=10 \end{gathered}[/tex]
Then square the result, we have
[tex]\begin{gathered} 10^2=100 \\ \text{hence } \\ n=100 \end{gathered}[/tex]
Then the complete trinomial of the polynomial becomes
[tex]u^2+20u+100[/tex]
To factor as a square of a binomial we use the perfect square trinomial above
[tex]\begin{gathered} u^2+20u+100 \\ u^2+20u+10^2 \\ \text{Then} \\ (u+10)^2 \end{gathered}[/tex]
Therefore
The vaue of n = 100
The factor as the square of a binomial is (u+ 10)²
