Answer :
To write the polynomial in standard form, we need to arrange its terms by the degree of the variable [tex]\( x \)[/tex], from the highest to the lowest degree.
Given the polynomial:
[tex]\[ 9x^2 + 5x + 27 + 2x^3 \][/tex]
Let's list the terms with their corresponding degrees:
- [tex]\( 2x^3 \)[/tex]: This term has a degree of 3.
- [tex]\( 9x^2 \)[/tex]: This term has a degree of 2.
- [tex]\( 5x \)[/tex]: This term has a degree of 1.
- [tex]\( 27 \)[/tex]: This term is a constant, with a degree of 0.
To create the standard form, arrange the terms in descending order of their degrees:
1. Start with the highest degree term, [tex]\( 2x^3 \)[/tex].
2. Next, include the term with degree 2, [tex]\( 9x^2 \)[/tex].
3. Then, add the term with degree 1, [tex]\( 5x \)[/tex].
4. Finally, include the constant term, [tex]\( 27 \)[/tex].
This gives us the standard form of the polynomial:
[tex]\[ 2x^3 + 9x^2 + 5x + 27 \][/tex]
This arrangement ensures the polynomial is in its standard form, ordered from the highest degree to the lowest.
Given the polynomial:
[tex]\[ 9x^2 + 5x + 27 + 2x^3 \][/tex]
Let's list the terms with their corresponding degrees:
- [tex]\( 2x^3 \)[/tex]: This term has a degree of 3.
- [tex]\( 9x^2 \)[/tex]: This term has a degree of 2.
- [tex]\( 5x \)[/tex]: This term has a degree of 1.
- [tex]\( 27 \)[/tex]: This term is a constant, with a degree of 0.
To create the standard form, arrange the terms in descending order of their degrees:
1. Start with the highest degree term, [tex]\( 2x^3 \)[/tex].
2. Next, include the term with degree 2, [tex]\( 9x^2 \)[/tex].
3. Then, add the term with degree 1, [tex]\( 5x \)[/tex].
4. Finally, include the constant term, [tex]\( 27 \)[/tex].
This gives us the standard form of the polynomial:
[tex]\[ 2x^3 + 9x^2 + 5x + 27 \][/tex]
This arrangement ensures the polynomial is in its standard form, ordered from the highest degree to the lowest.
