College

Write [tex]-34 x + 9 x^4 + 3 x^7 - 4 x^2[/tex] in standard form.

A. [tex]3 x^7 + 9 x^4 - 4 x^2 - 34 x[/tex]
B. [tex]9 x^4 + 3 x^7 - 4 x^2 - 34 x[/tex]
C. [tex]-4 x^2 + 9 x^4 + 3 x^7 - 34 x[/tex]
D. [tex]3 x^7 - 4 x^2 + 9 x^4 - 34 x[/tex]

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.

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