Answer :
To rewrite the expression [tex]\(4x - 9 + 7x^2 - 8x^3\)[/tex] in standard form, we need to arrange the terms in order of decreasing powers of [tex]\(x\)[/tex]. Here's how you do it:
1. Identify the Terms: Begin by taking note of each term:
- [tex]\( -8x^3 \)[/tex]
- [tex]\( 7x^2 \)[/tex]
- [tex]\( 4x \)[/tex]
- [tex]\( -9 \)[/tex]
2. Order by Power of [tex]\(x\)[/tex]: List these terms starting with the highest power of [tex]\(x\)[/tex] down to the constant:
- The term with [tex]\(x^3\)[/tex] is [tex]\( -8x^3 \)[/tex].
- The term with [tex]\(x^2\)[/tex] is [tex]\( 7x^2 \)[/tex].
- The term with [tex]\(x\)[/tex] is [tex]\( 4x \)[/tex].
- The constant term is [tex]\( -9 \)[/tex].
3. Write the Polynomial in Standard Form: Place the terms in descending order of power:
[tex]\[
-8x^3 + 7x^2 + 4x - 9
\][/tex]
Now, let's match this with the given options:
- Option 1: [tex]\(-8x^3 + 7x^2 + 4x - 9\)[/tex]
This rearranged expression in standard form matches Option 1. Therefore, the correct expression in standard form is:
[tex]\(-8x^3 + 7x^2 + 4x - 9\)[/tex]
1. Identify the Terms: Begin by taking note of each term:
- [tex]\( -8x^3 \)[/tex]
- [tex]\( 7x^2 \)[/tex]
- [tex]\( 4x \)[/tex]
- [tex]\( -9 \)[/tex]
2. Order by Power of [tex]\(x\)[/tex]: List these terms starting with the highest power of [tex]\(x\)[/tex] down to the constant:
- The term with [tex]\(x^3\)[/tex] is [tex]\( -8x^3 \)[/tex].
- The term with [tex]\(x^2\)[/tex] is [tex]\( 7x^2 \)[/tex].
- The term with [tex]\(x\)[/tex] is [tex]\( 4x \)[/tex].
- The constant term is [tex]\( -9 \)[/tex].
3. Write the Polynomial in Standard Form: Place the terms in descending order of power:
[tex]\[
-8x^3 + 7x^2 + 4x - 9
\][/tex]
Now, let's match this with the given options:
- Option 1: [tex]\(-8x^3 + 7x^2 + 4x - 9\)[/tex]
This rearranged expression in standard form matches Option 1. Therefore, the correct expression in standard form is:
[tex]\(-8x^3 + 7x^2 + 4x - 9\)[/tex]
