Answer :
To arrange the polynomial in descending order, we need to list the terms from the highest to the lowest power of [tex]\( x \)[/tex]. The given polynomial is:
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Let's identify the exponents for each term:
1. [tex]\( 4x^{12} \)[/tex] has an exponent of [tex]\( 12 \)[/tex].
2. [tex]\( 9x^7 \)[/tex] has an exponent of [tex]\( 7 \)[/tex].
3. [tex]\( 3x^3 \)[/tex] has an exponent of [tex]\( 3 \)[/tex].
4. [tex]\( -x \)[/tex] can be written as [tex]\( -1x^1 \)[/tex], with an exponent of [tex]\( 1 \)[/tex].
Next, we rearrange the terms in order from the highest exponent to the lowest:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Now, let's match this with the options provided:
A. [tex]\( 4x^{12} + 3x^3 - x + 9x^7 \)[/tex]
B. [tex]\( 9x^7 + 4x^{12} + 3x^3 - x \)[/tex]
C. [tex]\( 3x^3 + 4x^{12} + 9x^7 - x \)[/tex]
D. [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex]
The correct answer choice is:
D. [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex]
[tex]\[ 3x^3 + 9x^7 - x + 4x^{12} \][/tex]
Let's identify the exponents for each term:
1. [tex]\( 4x^{12} \)[/tex] has an exponent of [tex]\( 12 \)[/tex].
2. [tex]\( 9x^7 \)[/tex] has an exponent of [tex]\( 7 \)[/tex].
3. [tex]\( 3x^3 \)[/tex] has an exponent of [tex]\( 3 \)[/tex].
4. [tex]\( -x \)[/tex] can be written as [tex]\( -1x^1 \)[/tex], with an exponent of [tex]\( 1 \)[/tex].
Next, we rearrange the terms in order from the highest exponent to the lowest:
[tex]\[ 4x^{12} + 9x^7 + 3x^3 - x \][/tex]
Now, let's match this with the options provided:
A. [tex]\( 4x^{12} + 3x^3 - x + 9x^7 \)[/tex]
B. [tex]\( 9x^7 + 4x^{12} + 3x^3 - x \)[/tex]
C. [tex]\( 3x^3 + 4x^{12} + 9x^7 - x \)[/tex]
D. [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex]
The correct answer choice is:
D. [tex]\( 4x^{12} + 9x^7 + 3x^3 - x \)[/tex]
