College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Which polynomial is in standard form?

A. [tex]2x^4 + 6 + 24x^5[/tex]

B. [tex]6x^2 - 9x^3 + 12x^4[/tex]

C. [tex]19x + 6x^2 + 2[/tex]

D. [tex]23x^9 - 12x^4 + 19[/tex]

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]