Answer :
To determine the type of polynomial given by [tex]\(6x^3 + 3x^7 - 9\)[/tex], we should count the number of terms it has.
Here's how we can classify polynomials based on the number of terms:
1. Monomial: A polynomial with only one term. For example, [tex]\(5x^2\)[/tex] is a monomial.
2. Binomial: A polynomial with two terms. For instance, [tex]\(3x + 7\)[/tex] is a binomial.
3. Trinomial: A polynomial with three terms. An example of this is [tex]\(x^2 + 2x + 1\)[/tex].
Now, let's examine the polynomial [tex]\(6x^3 + 3x^7 - 9\)[/tex]:
- The first term is [tex]\(6x^3\)[/tex].
- The second term is [tex]\(3x^7\)[/tex].
- The third term is [tex]\(-9\)[/tex].
Since there are three terms in this polynomial, it is classified as a Trinomial.
Here's how we can classify polynomials based on the number of terms:
1. Monomial: A polynomial with only one term. For example, [tex]\(5x^2\)[/tex] is a monomial.
2. Binomial: A polynomial with two terms. For instance, [tex]\(3x + 7\)[/tex] is a binomial.
3. Trinomial: A polynomial with three terms. An example of this is [tex]\(x^2 + 2x + 1\)[/tex].
Now, let's examine the polynomial [tex]\(6x^3 + 3x^7 - 9\)[/tex]:
- The first term is [tex]\(6x^3\)[/tex].
- The second term is [tex]\(3x^7\)[/tex].
- The third term is [tex]\(-9\)[/tex].
Since there are three terms in this polynomial, it is classified as a Trinomial.
