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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.
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.
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