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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

Determine the value of n that makes the polynomial a perfect square trinomial. Then-example-1
User FRIDDAY
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1 Answer

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SOLUTION

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

User Yevhen Kuzmovych
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