The expression you provided is:

\[
12 + 21x - 6x^2
\]

This is a quadratic expression in terms of \( x \), which means it is a polynomial of degree 2.

### Standard form of a quadratic expression:
\[
ax^2 + bx + c
\]
For the expression \( 12 + 21x - 6x^2 \), we can rewrite it as:
\[
-6x^2 + 21x + 12
\]

Here:
- \( a = -6 \)
- \( b = 21 \)
- \( c = 12 \)

This expression cannot be simplified further, but we can explore its roots, factorization, or even graph its corresponding parabola.

Would you like to:
1. Find the roots (solve for \( x \))?
2. Factor the quadratic expression?
3. Analyze the vertex and axis of symmetry of the parabola?
4. Find the y-intercept and x-intercepts?
5. Graph this quadratic function?

**Tip:** The coefficient of \( x^2 \) determines whether the parabola opens upwards or downwards. Here, since \( -6 \) is negative, the parabola opens downward.

Explore how to work with the quadratic expression 12 + 21x - 6x^2. Learn key algebraic concepts such as polynomial degrees, the standard quadratic form, and how to analyze the parabola formed by the expression. Suitable for students in Grades 9-10.

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