ACTIVITY 1 [12] Polynomials are named by the highest exponent of the variable as well as the number of terms. example, \( x^{5}-3 x^{2}-1 \) is a quintic trinomial. Quintic is for the exponent 5 , which is the highes while trinomial implies three term. Using the above example, name the following polynomial expressions: \[ \begin{array}{l} 4 x^{2}+x-3 \\ \frac{3}{5} v^{2}\left(3 v^{2}-9\right) \\ k-6 k+12 k^{2}-3 k^{5} \\ -8 \\ 36 m^{6}-9 n^{2} \\ 5-9 y \end{array} \] \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \)

The first polynomial, \( 4x^{2}+x-3 \), is a quadratic trinomial since its highest exponent is 2 and there are three terms. Next, the expression \( \frac{3}{5} v^{2}(3 v^{2}-9) \), when expanded, yields \( \frac{9}{5} v^{4} - \frac{27}{5} v^{2} \), which is a quartic binomial due to the highest exponent of 4 and two terms. Moving on, \( k - 6k + 12k^{2} - 3k^{5} \) can be rearranged to \( -3k^{5} + 12k^{2} - 5k \) highlighting that it's a quintic trinomial with a highest exponent of 5 and three terms. The constant term \(-8\) stands alone and is simply a constant polynomial, which is a degree of 0. For \( 36m^{6} - 9n^{2} \), the highest exponent is 6 concerning \( m \), making this a sextic binomial with two terms. Finally, in the expression \( 5 - 9y \), the highest exponent is 1, so it’s a linear binomial. Here’s the final tally: 1. \( 4x^{2}+x-3 \) - Quadratic Trinomial 2. \( \frac{3}{5} v^{2}(3 v^{2}-9) \) - Quartic Binomial 3. \( k - 6k + 12k^{2} - 3k^{5} \) - Quintic Trinomial 4. \(-8\) - Constant Polynomial 5. \( 36m^{6}-9n^{2} \) - Sextic Binomial 6. \( 5-9y \) - Linear Binomial