College

Write the polynomial in standard form. Then classify the polynomial by degree and by number of terms.

[tex]7x^4 + 9x^4 - 6x^4[/tex]

Write the polynomial in standard form.
[tex]\square[/tex] (Simplify your answer.)

Answer :

To write the polynomial in standard form and classify it by degree and the number of terms, we start by simplifying the given expression [tex]\(7x^4 + 9x^4 - 6x^4\)[/tex].

Step 1: Combine Like Terms

- All terms in the polynomial have the same degree of [tex]\(x^4\)[/tex].
- To simplify, combine the coefficients of [tex]\(x^4\)[/tex]:
[tex]\((7 + 9 - 6)x^4 = 10x^4\)[/tex].

So, the polynomial in standard form is [tex]\(\boxed{10x^4}\)[/tex].

Step 2: Classify the Polynomial by Degree

- The degree of a polynomial is the highest exponent of the variable in the polynomial.
- In [tex]\(10x^4\)[/tex], the exponent is 4.

Thus, the degree of the polynomial is 4.

Step 3: Classify the Polynomial by Number of Terms

- The number of terms in a polynomial is referred to as either a monomial (1 term), binomial (2 terms), or trinomial (3 terms). If there are more than three terms, it is simply called a polynomial with that number of terms.
- The simplified polynomial [tex]\(10x^4\)[/tex] consists of only one term.

Therefore, it is classified as a monomial.

In summary, the polynomial in standard form is [tex]\(\boxed{10x^4}\)[/tex], it has a degree of 4, and it is a monomial.