Question

Question
Express in simplest form: 36x−216x2−36
.(1 point)
Responses

36x+6
Start Fraction 36 over x plus 6 End Fraction

20x
Start Fraction 20 over x End Fraction

36x−6
Start Fraction 36 over x minus 6 End Fraction

6x
Start Fraction 6 over x End Fraction
Skip to navigation

Answer 1

To simplify the expression \( 36x - 216x^2 - 36 \), let's first factor it.

1. We can rearrange the expression:
\[
-216x^2 + 36x - 36
\]

2. Factor out the common factor of \(-36\):
\[
-36(6x^2 - x + 1)
\]

3. Now, let's check if \( 6x^2 - x + 1 \) can be factored further. To do this, we will need to check the discriminant \( b^2 - 4ac \):
- Here, \( a = 6 \), \( b = -1 \), and \( c = 1 \):
\[
(-1)^2 - 4 \cdot 6 \cdot 1 = 1 - 24 = -23
\]

Since the discriminant is negative, \( 6x^2 - x + 1 \) cannot be factored further over the real numbers.

Thus the expression \( 36x - 216x^2 - 36 \) simplifies to:
\[
-36(6x^2 - x + 1)
\]

After further analysis, it appears we might have misinterpreted the task of the problem. If the intention was to check for simpler forms rather than factoring, we can observe whether the expression represents a simplified form of the expression stated.

With the options provided, none seem to match the simplest form we analyzed in relation to the expression resembling a polynomial calculation.

Would you like to clarify the context or restrict further simplification to a certain framework?