Which of the following values of c will make the expression x2 - 12x + c a perfect square trinomial?
Question
Which of the following values of c will make the expression x² - 12x + c a perfect square trinomial?
Solution
A perfect square trinomial is a trinomial that can be factored into the square of a binomial. In other words, it can be written in the form (ax+b)^2.
The general form of a perfect square trinomial is x^2 + 2ax + a^2.
Given the trinomial x^2 - 12x + c, we can see that the coefficient of x is -12. This is the 2a term in the general form, so a = -12/2 = -6.
The constant term in a perfect square trinomial is a^2. So, we square -6 to get 36.
Therefore, the value of c that makes x^2 - 12x + c a perfect square trinomial is 36.
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