Polynomials are named by the highest exponent of the variable as well as the number of terms. For example, \( x^{5}-3 x^{2}-1 \) is a quintic trinomial. Quintic is for the exponent 5 , which is the highest, while trinomial implies three term. Using the above example, name the following polynomial expressions: \[ \begin{array}{ll} 1.1 & 4 x^{2}+x-3 \\ 1.2 & \frac{3}{5} v^{2}\left(3 v^{2}-9\right) \\ 1.3 & k-6 k+12 k^{2}-3 k^{5} \\ 1.4 & -8 \\ 1.5 & 36 m^{6}-9 n^{2} \\ 1.6 & 5-9 y \end{array} \] \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \)
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1.1: This expression is a quadratic trinomial since the highest exponent is 2 and there are three terms. 1.2: Here, we first need to expand the expression, which yields \( \frac{9}{5}v^{4} - \frac{27}{5}v^{2} \). The resulting polynomial is a quartic binomial because the highest exponent is 4 and there are two terms after expansion. 1.3: This polynomial can be rearranged to \( -3k^{5} + 12k^{2} - 6k \), which identifies it as a quintic trinomial, as the highest exponent is 5 with three terms. 1.4: The expression \(-8\) is a constant polynomial. It has no variable and can be classified as a zero-degree polynomial because its highest exponent is 0. 1.5: This polynomial can be expressed as \( 36m^{6} - 9n^{2} \), making it a sixth degree binomial since the highest exponent is 6 and it contains two terms. 1.6: The expression \( 5 - 9y \) is classified as a linear binomial. The highest exponent is 1, and it consists of two terms.
