Question

simplify the expression:
3k² + 2k + 9

Explanation:

Step1: Check for like terms

The expression is \(3k^{2}+2k + 9\). The terms \(3k^{2}\), \(2k\), and \(9\) are all unlike terms (different powers of \(k\) or constant).

Step2: Determine if it can be factored

For a quadratic \(ax^{2}+bx + c\) (here \(a = 3\), \(b=2\), \(c = 9\)), the discriminant is \(b^{2}-4ac=(2)^{2}-4\times3\times9=4 - 108=- 104\), which is negative. So it cannot be factored over the real numbers.

Step3: Conclusion

Since there are no like terms to combine and it cannot be factored (over reals), the expression is already in its simplest form.

Answer:

\(3k^{2}+2k + 9\)