Answer :
To determine which polynomial is in standard form, we need to arrange each polynomial with its terms in descending order of the exponents of [tex]\( x \)[/tex].
Let's examine each of the given polynomials:
1. [tex]\( 2x^4 + 6 + 24x^5 \)[/tex]:
- This polynomial is currently written as [tex]\( 2x^4 + 6 + 24x^5 \)[/tex].
- To put it in standard form, order the terms by the power of [tex]\( x \)[/tex]: [tex]\( 24x^5 + 2x^4 + 6 \)[/tex].
2. [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex]:
- This polynomial is currently written as [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex].
- To put it in standard form, order the terms by the power of [tex]\( x \)[/tex]: [tex]\( 12x^4 - 9x^3 + 6x^2 \)[/tex].
3. [tex]\( 19x + 6x^2 + 2 \)[/tex]:
- This polynomial is currently written as [tex]\( 19x + 6x^2 + 2 \)[/tex].
- To put it in standard form, order the terms by the power of [tex]\( x \)[/tex]: [tex]\( 6x^2 + 19x + 2 \)[/tex].
4. [tex]\( 23x^9 - 12x^4 + 19 \)[/tex]:
- This polynomial is currently written as [tex]\( 23x^9 - 12x^4 + 19 \)[/tex].
- The terms are already in descending order of the powers of [tex]\( x \)[/tex]: [tex]\( 9, 4, 0 \)[/tex].
The fourth polynomial, [tex]\( 23x^9 - 12x^4 + 19 \)[/tex], is already in standard form because its terms are arranged correctly from highest to lowest power of [tex]\( x \)[/tex].
Therefore, the polynomial that is in standard form is:
[tex]\( 23x^9 - 12x^4 + 19 \)[/tex].
Let's examine each of the given polynomials:
1. [tex]\( 2x^4 + 6 + 24x^5 \)[/tex]:
- This polynomial is currently written as [tex]\( 2x^4 + 6 + 24x^5 \)[/tex].
- To put it in standard form, order the terms by the power of [tex]\( x \)[/tex]: [tex]\( 24x^5 + 2x^4 + 6 \)[/tex].
2. [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex]:
- This polynomial is currently written as [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex].
- To put it in standard form, order the terms by the power of [tex]\( x \)[/tex]: [tex]\( 12x^4 - 9x^3 + 6x^2 \)[/tex].
3. [tex]\( 19x + 6x^2 + 2 \)[/tex]:
- This polynomial is currently written as [tex]\( 19x + 6x^2 + 2 \)[/tex].
- To put it in standard form, order the terms by the power of [tex]\( x \)[/tex]: [tex]\( 6x^2 + 19x + 2 \)[/tex].
4. [tex]\( 23x^9 - 12x^4 + 19 \)[/tex]:
- This polynomial is currently written as [tex]\( 23x^9 - 12x^4 + 19 \)[/tex].
- The terms are already in descending order of the powers of [tex]\( x \)[/tex]: [tex]\( 9, 4, 0 \)[/tex].
The fourth polynomial, [tex]\( 23x^9 - 12x^4 + 19 \)[/tex], is already in standard form because its terms are arranged correctly from highest to lowest power of [tex]\( x \)[/tex].
Therefore, the polynomial that is in standard form is:
[tex]\( 23x^9 - 12x^4 + 19 \)[/tex].
