Question
Find the value of \( n \) so that the expression is a perfect square trinomial. Then factor the trinomial, \[ c^{2}-12 c+n \] Part: \( 0 / 2 \) Part 1 of 2 Determine the value of \( n \)
Ask by Hobbs Little. in the United States
Feb 08,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( n = 36 \)
Solution
For a trinomial of the form c² - 12c + n to be a perfect square, it must have the form (c - a)², where (c - a)² expands to c² - 2ac + a².
We can equate the coefficient of c in our expression with -2a:
-2a = -12
a = 6
Then, the constant term must be:
a² = 6² = 36
Thus, n should be 36.
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Simplify this solution Mind Expander
To make the expression \( c^{2}-12c+n \) a perfect square trinomial, we can use the formula for a perfect square trinomial, which is \( (c-a)^2 = c^2 - 2ac + a^2 \). In our case, we see that \( -12c \) corresponds to the term \( -2ac \). Setting \( -2a = -12 \) gives us \( a = 6 \). Now we can find \( n \) by substituting \( a \) back into the perfect square trinomial formula, specifically, \( n = a^2 \). Thus, \( n = 6^2 = 36 \). So, the value of \( n \) is \( 36 \).
