Find the Perfect Square Trinomial x^2-18x

Problem

x2−18*x

Solution

1. Identify the coefficient of the linear term, which is the value b in the quadratic expression x2+b*x

b=−18

2. Divide the coefficient b by 2 to find the value needed for the binomial square.

b/2=(−18)/2=−9

3. Square this result to determine the constant term c that completes the perfect square trinomial.

c=(−9)2=81

4. Add the constant term to the original expression to form the perfect square trinomial.

x2−18*x+81

5. Factor the resulting trinomial into the square of a binomial.

(x−9)2

Final Answer

x2−18*x+81=(x−9)2

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