Answer :
To write the polynomial [tex]\(-7 + 2x - x^5 + 4x^4 + 2x^3\)[/tex] in standard form, you'll want to arrange the terms in order of descending powers of [tex]\(x\)[/tex]. Let's go through this step-by-step:
1. Identify the terms and their exponents:
- [tex]\(-x^5\)[/tex] is the term with [tex]\(x^5\)[/tex].
- [tex]\(4x^4\)[/tex] is the term with [tex]\(x^4\)[/tex].
- [tex]\(2x^3\)[/tex] is the term with [tex]\(x^3\)[/tex].
- [tex]\(2x\)[/tex] is the term with [tex]\(x^1\)[/tex].
- [tex]\(-7\)[/tex] is the constant term with no [tex]\(x\)[/tex].
2. Order the terms: Start by placing the term with the highest power of [tex]\(x\)[/tex] first, and then proceed in descending order.
- The term with the highest power is [tex]\(-x^5\)[/tex].
- Next is [tex]\(4x^4\)[/tex].
- Then [tex]\(2x^3\)[/tex].
- Then [tex]\(2x\)[/tex].
- Finally, the constant term [tex]\(-7\)[/tex].
3. Write the polynomial in standard form: Arrange the terms from step 2:
[tex]\[
-x^5 + 4x^4 + 2x^3 + 2x - 7
\][/tex]
This is the polynomial written in standard form, ordered by descending powers of [tex]\(x\)[/tex].
1. Identify the terms and their exponents:
- [tex]\(-x^5\)[/tex] is the term with [tex]\(x^5\)[/tex].
- [tex]\(4x^4\)[/tex] is the term with [tex]\(x^4\)[/tex].
- [tex]\(2x^3\)[/tex] is the term with [tex]\(x^3\)[/tex].
- [tex]\(2x\)[/tex] is the term with [tex]\(x^1\)[/tex].
- [tex]\(-7\)[/tex] is the constant term with no [tex]\(x\)[/tex].
2. Order the terms: Start by placing the term with the highest power of [tex]\(x\)[/tex] first, and then proceed in descending order.
- The term with the highest power is [tex]\(-x^5\)[/tex].
- Next is [tex]\(4x^4\)[/tex].
- Then [tex]\(2x^3\)[/tex].
- Then [tex]\(2x\)[/tex].
- Finally, the constant term [tex]\(-7\)[/tex].
3. Write the polynomial in standard form: Arrange the terms from step 2:
[tex]\[
-x^5 + 4x^4 + 2x^3 + 2x - 7
\][/tex]
This is the polynomial written in standard form, ordered by descending powers of [tex]\(x\)[/tex].
