Question

simplify the expression:
3k² + 2k + 9

Explanation:

Step1: Check for like terms

The expression is \(3k^{2}+2k + 9\). The terms are \(3k^{2}\) (quadratic term), \(2k\) (linear term), and \(9\) (constant term). There are no like terms (terms with the same power of \(k\)) to combine.

Step2: Determine if it can be factored

We check if the quadratic trinomial \(3k^{2}+2k + 9\) 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 does not factor over the real numbers.

Answer:

The expression \(3k^{2}+2k + 9\) is already in its simplest form as there are no like terms to combine and it cannot be factored over the real numbers, so the simplified form is \(3k^{2}+2k + 9\).