Answer :
Sure! Let's simplify the polynomial and then classify it by its degree and number of terms.
1. Write the Polynomial in Standard Form:
The given polynomial is [tex]\(5x^4 + 9x^4 - 6x^4\)[/tex].
To simplify, we need to combine the like terms. Since all terms are multiples of [tex]\(x^4\)[/tex], we simply add or subtract the coefficients:
[tex]\[
5x^4 + 9x^4 - 6x^4 = (5 + 9 - 6)x^4
\][/tex]
Calculate the sum of the coefficients:
[tex]\[
5 + 9 - 6 = 8
\][/tex]
Therefore, the polynomial in standard form is:
[tex]\[
8x^4
\][/tex]
2. Classify the Polynomial by Degree:
The degree of a polynomial is the highest power of the variable present in the polynomial. In this case, the highest power of [tex]\(x\)[/tex] is 4, so the degree of this polynomial is 4.
3. Classify the Polynomial by Number of Terms:
The number of terms in a polynomial is determined by counting the separate expressions separated by addition or subtraction. The simplified polynomial [tex]\(8x^4\)[/tex] has only one term.
In summary:
- The polynomial in standard form is [tex]\(8x^4\)[/tex].
- The degree of the polynomial is 4.
- The polynomial is a monomial because it has one term.
1. Write the Polynomial in Standard Form:
The given polynomial is [tex]\(5x^4 + 9x^4 - 6x^4\)[/tex].
To simplify, we need to combine the like terms. Since all terms are multiples of [tex]\(x^4\)[/tex], we simply add or subtract the coefficients:
[tex]\[
5x^4 + 9x^4 - 6x^4 = (5 + 9 - 6)x^4
\][/tex]
Calculate the sum of the coefficients:
[tex]\[
5 + 9 - 6 = 8
\][/tex]
Therefore, the polynomial in standard form is:
[tex]\[
8x^4
\][/tex]
2. Classify the Polynomial by Degree:
The degree of a polynomial is the highest power of the variable present in the polynomial. In this case, the highest power of [tex]\(x\)[/tex] is 4, so the degree of this polynomial is 4.
3. Classify the Polynomial by Number of Terms:
The number of terms in a polynomial is determined by counting the separate expressions separated by addition or subtraction. The simplified polynomial [tex]\(8x^4\)[/tex] has only one term.
In summary:
- The polynomial in standard form is [tex]\(8x^4\)[/tex].
- The degree of the polynomial is 4.
- The polynomial is a monomial because it has one term.
