Pregunta
Determine what c -value will create a perfect square trinomial for the following expression: \( x^{2}+18 x+c \)
Ask by Higgins Chang. in the United States
Feb 27,2025
Solución de inteligencia artificial de Upstudy
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c = 81
Solución
A perfect square trinomial takes the form (x + k)² = x² + 2kx + k². In the given expression x² + 18x + c, you can match the coefficient of x (which is 18) to 2k. So, set 2k = 18 which gives k = 9. Then, k² = 9² = 81.
Thus, the value of c must be 81 for the expression to become a perfect square trinomial.
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Simplifique esta solución Mind Expander
To create a perfect square trinomial from the expression \( x^{2} + 18x + c \), you need to take half of the coefficient of \( x \) (which is 18), square it, and then add that value for \( c \). Half of 18 is 9, and squaring it gives \( 9^2 = 81 \). Therefore, the value of \( c \) that will create a perfect square trinomial is 81. Now, the expression can be rewritten as \( (x + 9)^2 \), which confirms that it is a perfect square trinomial.
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