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Answer :
To create the expression using the given terms and numbers, let's break it down step by step. You are provided with a polynomial expression and some additional numbers and terms. The task is to understand how the expression is constructed.
The initial expression is:
[tex]\[ 8x^5 - 4x^4 - 72x^3 + 60x^2. \][/tex]
We'll identify the coefficients and the terms that each coefficient is paired with:
1. Coefficient 8: This is paired with the term [tex]\( x^5 \)[/tex], forming the term [tex]\( 8x^5 \)[/tex].
2. Coefficient -4: This goes with [tex]\( x^4 \)[/tex], forming the term [tex]\( -4x^4 \)[/tex].
3. Coefficient -72: This is paired with [tex]\( x^3 \)[/tex], resulting in [tex]\( -72x^3 \)[/tex].
4. Coefficient 60: This is coupled with [tex]\( x^2 \)[/tex], giving us [tex]\( 60x^2 \)[/tex].
The numbers provided: 1, 4, 15, 18, 60, 72, and powers of [tex]\( x \)[/tex]: [tex]\( x \)[/tex], [tex]\( x^2 \)[/tex], [tex]\( x^3 \)[/tex], [tex]\( x^4 \)[/tex]. In this problem, we already see how the coefficients align with the powers of [tex]\( x \)[/tex] provided with the initial expression.
The expression as written is complete, which means that we just need to confirm that each coefficient is already correctly aligned with its term:
- [tex]\( 8 \)[/tex] with [tex]\( x^5 \)[/tex],
- [tex]\(-4\)[/tex] with [tex]\( x^4 \)[/tex],
- [tex]\(-72\)[/tex] with [tex]\( x^3 \)[/tex],
- [tex]\( 60 \)[/tex] with [tex]\( x^2 \)[/tex].
No additional [tex]\( x \)[/tex] terms are necessary in this expression, considering how the coefficients and powers are sufficiently paired in the expression provided.
Thus, the expression [tex]\( 8x^5 - 4x^4 - 72x^3 + 60x^2 \)[/tex] uses the coefficients and terms correctly, and no additional adjustments are needed based on the options given. The expression is complete and factually accurate.
The initial expression is:
[tex]\[ 8x^5 - 4x^4 - 72x^3 + 60x^2. \][/tex]
We'll identify the coefficients and the terms that each coefficient is paired with:
1. Coefficient 8: This is paired with the term [tex]\( x^5 \)[/tex], forming the term [tex]\( 8x^5 \)[/tex].
2. Coefficient -4: This goes with [tex]\( x^4 \)[/tex], forming the term [tex]\( -4x^4 \)[/tex].
3. Coefficient -72: This is paired with [tex]\( x^3 \)[/tex], resulting in [tex]\( -72x^3 \)[/tex].
4. Coefficient 60: This is coupled with [tex]\( x^2 \)[/tex], giving us [tex]\( 60x^2 \)[/tex].
The numbers provided: 1, 4, 15, 18, 60, 72, and powers of [tex]\( x \)[/tex]: [tex]\( x \)[/tex], [tex]\( x^2 \)[/tex], [tex]\( x^3 \)[/tex], [tex]\( x^4 \)[/tex]. In this problem, we already see how the coefficients align with the powers of [tex]\( x \)[/tex] provided with the initial expression.
The expression as written is complete, which means that we just need to confirm that each coefficient is already correctly aligned with its term:
- [tex]\( 8 \)[/tex] with [tex]\( x^5 \)[/tex],
- [tex]\(-4\)[/tex] with [tex]\( x^4 \)[/tex],
- [tex]\(-72\)[/tex] with [tex]\( x^3 \)[/tex],
- [tex]\( 60 \)[/tex] with [tex]\( x^2 \)[/tex].
No additional [tex]\( x \)[/tex] terms are necessary in this expression, considering how the coefficients and powers are sufficiently paired in the expression provided.
Thus, the expression [tex]\( 8x^5 - 4x^4 - 72x^3 + 60x^2 \)[/tex] uses the coefficients and terms correctly, and no additional adjustments are needed based on the options given. The expression is complete and factually accurate.
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