Answer
The answers for the Polynomial Types and Degrees are highlighted in the table in blue.
Work Step by Step
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.
