Question

Determine the value of n that makes the polynomial a perfect square trinomial. Then factor as the square of a binomial. Express numbers as integers orsimplified fractions.u^2+20u+n

Answer 1

The expression is given as

`u^2+20u+n`

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

`\begin{gathered} \text{the coefficient of u=20} \\ \text{divide by 2=}\frac{\text{20}}{2}=10 \end{gathered}`

Then square the result, we have

`\begin{gathered} 10^2=100 \\ \text{hence } \\ n=100 \end{gathered}`

Then the complete trinomial of the polynomial becomes

`u^2+20u+100`

To factor as a square of a binomial we use the perfect square trinomial above

`\begin{gathered} u^2+20u+100 \\ u^2+20u+10^2 \\ \text{Then} \\ (u+10)^2 \end{gathered}`

Therefore

The vaue of n = 100

The factor as the square of a binomial is (u+ 10)²