## Algebra: A Combined Approach (4th Edition)

Each equation given asks for a Polynomial Type and its degree. As shown in the table, Equation (a). $-6x + 14$ is a binomial because it has 2 terms, which are $-6x$ for one and the other is 14. Hence, 2 terms. It is helpful to also remember that the prefix of each Polynomial type each signifies a certain number: In the Polynomial type monomial, its prefix is mono-, meaning 1. So, monomials only have 1 term in an equation. The prefix bi- for binomial means 2. So, binomials have 2 terms in an equation. The prefix tri- for trinomials means 3. So, trinomials have 3 terms in an equation. Based on this, equation (b). $9x$ $- 3x^{6}$ + $5x^{4}$ $+2$ has 4 terms, which means it is neither a monomial, binomial, nor trinomial. But equation (c) $10x^{2}$ – $6x$ $– 6$ has 3 terms, so it is a trinomial. As for degrees, we are looking for the highest exponent listed in each polynomial. For equation (a). $-6x + 14$, the highest exponent is 1. We can rule out the term 14 in the equation, because it is a Constant, and its exponent is 0. So, $-6x$ is the term that provides the highest degree of 1. This is because of $x$. Even though $x$ does not show an exponent visibly, it nevertheless has an assumed degree of 1. Equation (b). 9$x$ $- 3x^{6}$ + $5x^{4}$ $+2$ has 4 terms, so the polynomial's highest degree (exponent) is 6, as seen in its term, $- 3x^{6}$. So, the answer is 6. Equation (c) $10x^{2}$ – $6x$ $– 6$ has 3 terms, and out of those 3, the highest exponent is 2 as seen in its term, $10x^{2}$. So, the trinomial's highest degree (exponent) is 2. So, the answer is 2.