Answer :
To write the polynomial in descending order, we need to arrange the terms based on the exponents of [tex]\( x \)[/tex], starting from the highest exponent to the lowest. Let's go through the process step-by-step:
Given polynomial:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
1. Identify the exponents of [tex]\( x \)[/tex] in each term:
- [tex]\( 3x^3 \)[/tex] has an exponent of 3.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( -x \)[/tex] can be written as [tex]\( -1x^1 \)[/tex] with an exponent of 1.
- [tex]\( 4x^{12} \)[/tex] has an exponent of 12.
2. Order the terms by descending exponent:
- The term with the highest exponent is [tex]\( 4x^{12} \)[/tex].
- The next highest is [tex]\( 9x^7 \)[/tex].
- Followed by [tex]\( 3x^3 \)[/tex].
- Lastly, the term [tex]\( -x \)[/tex] (or [tex]\( -1x^1 \)[/tex]) has the smallest exponent.
3. Write the polynomial with the terms in descending order of their exponents:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
So, the polynomial written in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Given polynomial:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
1. Identify the exponents of [tex]\( x \)[/tex] in each term:
- [tex]\( 3x^3 \)[/tex] has an exponent of 3.
- [tex]\( 9x^7 \)[/tex] has an exponent of 7.
- [tex]\( -x \)[/tex] can be written as [tex]\( -1x^1 \)[/tex] with an exponent of 1.
- [tex]\( 4x^{12} \)[/tex] has an exponent of 12.
2. Order the terms by descending exponent:
- The term with the highest exponent is [tex]\( 4x^{12} \)[/tex].
- The next highest is [tex]\( 9x^7 \)[/tex].
- Followed by [tex]\( 3x^3 \)[/tex].
- Lastly, the term [tex]\( -x \)[/tex] (or [tex]\( -1x^1 \)[/tex]) has the smallest exponent.
3. Write the polynomial with the terms in descending order of their exponents:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
So, the polynomial written in descending order is:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
