Answer :
To write the expression [tex]\(-34x + 9x^4 + 3x^7 - 4x^2\)[/tex] in standard form, we need to arrange the terms in order of decreasing powers of [tex]\(x\)[/tex]. Here’s how we do it:
1. Identify the Powers of [tex]\(x\)[/tex]:
- The term [tex]\(3x^7\)[/tex] has the highest power, which is 7.
- The term [tex]\(9x^4\)[/tex] has the next highest power, which is 4.
- The term [tex]\(-4x^2\)[/tex] has the power of 2.
- The term [tex]\(-34x\)[/tex] has the power of 1.
2. Arrange Terms in Descending Order of Powers:
- Start with the highest power term: [tex]\(3x^7\)[/tex].
- Next, place the [tex]\(9x^4\)[/tex] term.
- Then, place the [tex]\(-4x^2\)[/tex] term.
- Finally, place the [tex]\(-34x\)[/tex] term.
3. Write the Polynomial in Standard Form:
- The standard form is: [tex]\(3x^7 + 9x^4 - 4x^2 - 34x\)[/tex].
Given the options, the expression in standard form corresponds to:
A. [tex]\(3x^7 + 9x^4 - 4x^2 - 34x\)[/tex]
Thus, option A is the correct answer.
1. Identify the Powers of [tex]\(x\)[/tex]:
- The term [tex]\(3x^7\)[/tex] has the highest power, which is 7.
- The term [tex]\(9x^4\)[/tex] has the next highest power, which is 4.
- The term [tex]\(-4x^2\)[/tex] has the power of 2.
- The term [tex]\(-34x\)[/tex] has the power of 1.
2. Arrange Terms in Descending Order of Powers:
- Start with the highest power term: [tex]\(3x^7\)[/tex].
- Next, place the [tex]\(9x^4\)[/tex] term.
- Then, place the [tex]\(-4x^2\)[/tex] term.
- Finally, place the [tex]\(-34x\)[/tex] term.
3. Write the Polynomial in Standard Form:
- The standard form is: [tex]\(3x^7 + 9x^4 - 4x^2 - 34x\)[/tex].
Given the options, the expression in standard form corresponds to:
A. [tex]\(3x^7 + 9x^4 - 4x^2 - 34x\)[/tex]
Thus, option A is the correct answer.