Answer :
To determine which polynomial is in standard form, we need to check if the terms are arranged in descending order of their exponents. Let's review each polynomial step by step:
1. Polynomial: [tex]\( 2x^4 + 6 + 24x^5 \)[/tex]
- Terms: [tex]\( 24x^5, 2x^4, 6 \)[/tex]
- Order by power of [tex]\( x \)[/tex]: [tex]\( 24x^5, 2x^4, 6 \)[/tex]
- Ordered in descending order of exponents: Yes
2. Polynomial: [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex]
- Terms: [tex]\( 12x^4, -9x^3, 6x^2 \)[/tex]
- Order by power of [tex]\( x \)[/tex]: [tex]\( 12x^4, -9x^3, 6x^2 \)[/tex]
- Ordered in descending order of exponents: Yes
3. Polynomial: [tex]\( 19x + 6x^2 + 2 \)[/tex]
- Terms: [tex]\( 6x^2, 19x, 2 \)[/tex]
- Order by power of [tex]\( x \)[/tex]: [tex]\( 6x^2, 19x, 2 \)[/tex]
- Ordered in descending order of exponents: Yes
4. Polynomial: [tex]\( 23x^9 - 12x^4 + 19 \)[/tex]
- Terms: [tex]\( 23x^9, -12x^4, 19 \)[/tex]
- Order by power of [tex]\( x \)[/tex]: [tex]\( 23x^9, -12x^4, 19 \)[/tex]
- Ordered in descending order of exponents: Yes
After checking all the polynomials, it appears that all the polynomials given are in standard form. Each polynomial has its terms ordered in descending order of their powers.
Thus, the correct answer is that all the polynomials given are in standard form:
1. [tex]\( 2x^4 + 6 + 24x^5 \)[/tex]
2. [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex]
3. [tex]\( 19x + 6x^2 + 2 \)[/tex]
4. [tex]\( 23x^9 - 12x^4 + 19 \)[/tex]
1. Polynomial: [tex]\( 2x^4 + 6 + 24x^5 \)[/tex]
- Terms: [tex]\( 24x^5, 2x^4, 6 \)[/tex]
- Order by power of [tex]\( x \)[/tex]: [tex]\( 24x^5, 2x^4, 6 \)[/tex]
- Ordered in descending order of exponents: Yes
2. Polynomial: [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex]
- Terms: [tex]\( 12x^4, -9x^3, 6x^2 \)[/tex]
- Order by power of [tex]\( x \)[/tex]: [tex]\( 12x^4, -9x^3, 6x^2 \)[/tex]
- Ordered in descending order of exponents: Yes
3. Polynomial: [tex]\( 19x + 6x^2 + 2 \)[/tex]
- Terms: [tex]\( 6x^2, 19x, 2 \)[/tex]
- Order by power of [tex]\( x \)[/tex]: [tex]\( 6x^2, 19x, 2 \)[/tex]
- Ordered in descending order of exponents: Yes
4. Polynomial: [tex]\( 23x^9 - 12x^4 + 19 \)[/tex]
- Terms: [tex]\( 23x^9, -12x^4, 19 \)[/tex]
- Order by power of [tex]\( x \)[/tex]: [tex]\( 23x^9, -12x^4, 19 \)[/tex]
- Ordered in descending order of exponents: Yes
After checking all the polynomials, it appears that all the polynomials given are in standard form. Each polynomial has its terms ordered in descending order of their powers.
Thus, the correct answer is that all the polynomials given are in standard form:
1. [tex]\( 2x^4 + 6 + 24x^5 \)[/tex]
2. [tex]\( 6x^2 - 9x^3 + 12x^4 \)[/tex]
3. [tex]\( 19x + 6x^2 + 2 \)[/tex]
4. [tex]\( 23x^9 - 12x^4 + 19 \)[/tex]
