Question

If x²-32x+c is a perfect

square trinomial, what is the value of c?
O 16
O 32
O 256
O 1024

Answer 1

A perfect square trinomial is a quadratic trinomial that can be factored into the square of a binomial (a+b)^2. To find the value of c in the trinomial x^2 - 32x + c, we need to find the value of c that makes it a perfect square trinomial.

Step-by-step explanation:

A perfect square trinomial is a quadratic trinomial that can be factored into the square of a binomial (a+b)^2. To find the value of c in the trinomial x^2 - 32x + c, we need to find the value of c that makes it a perfect square trinomial. The middle term of the trinomial can be written as -2ab, where a is the coefficient of x and b is the coefficient of the square root of c. In this case, a = -32 and b = sqrt(c).

So, -2ab = -2(-32)(sqrt(c)) = 64(sqrt(c)). The original trinomial x^2 - 32x + c is a perfect square trinomial if 64(sqrt(c)) = -32x. Simplifying further, we get sqrt(c) = -x/2. Taking the square of both sides, c = (x/2)^2 = x^2/4.

Therefore, the value of c is x^2/4.

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