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Answer :
Certainly! Let's find the difference between the two polynomials step-by-step:
We have two polynomials:
1. [tex]\( P_1 = 9x^8 + 8x^7 + 9 \)[/tex]
2. [tex]\( P_2 = 6x^7 + 2x + 2 \)[/tex]
We need to calculate the difference [tex]\( P_1 - P_2 \)[/tex].
### Step 1: Align the polynomials by their powers of [tex]\( x \)[/tex].
Write down each polynomial with respect to the same powers of [tex]\( x \)[/tex]:
- For [tex]\( P_1 = 9x^8 + 8x^7 + 0x + 9 \)[/tex]
- For [tex]\( P_2 = 0x^8 + 6x^7 + 2x + 2 \)[/tex]
### Step 2: Subtract the corresponding terms.
Subtract the terms of [tex]\( P_2 \)[/tex] from the terms of [tex]\( P_1 \)[/tex]:
- For [tex]\( x^8 \)[/tex]:
- [tex]\( 9x^8 - 0x^8 = 9x^8 \)[/tex]
- For [tex]\( x^7 \)[/tex]:
- [tex]\( 8x^7 - 6x^7 = 2x^7 \)[/tex]
- For [tex]\( x \)[/tex]:
- [tex]\( 0x - 2x = -2x \)[/tex]
- For the constant term:
- [tex]\( 9 - 2 = 7 \)[/tex]
### Step 3: Write the resulting polynomial.
Putting it all together, the resulting polynomial after subtraction is:
[tex]\[ 9x^8 + 2x^7 - 2x + 7 \][/tex]
Therefore, the polynomial that represents the difference is option C:
[tex]\[ \boxed{9x^8 + 2x^7 - 2x + 7} \][/tex]
We have two polynomials:
1. [tex]\( P_1 = 9x^8 + 8x^7 + 9 \)[/tex]
2. [tex]\( P_2 = 6x^7 + 2x + 2 \)[/tex]
We need to calculate the difference [tex]\( P_1 - P_2 \)[/tex].
### Step 1: Align the polynomials by their powers of [tex]\( x \)[/tex].
Write down each polynomial with respect to the same powers of [tex]\( x \)[/tex]:
- For [tex]\( P_1 = 9x^8 + 8x^7 + 0x + 9 \)[/tex]
- For [tex]\( P_2 = 0x^8 + 6x^7 + 2x + 2 \)[/tex]
### Step 2: Subtract the corresponding terms.
Subtract the terms of [tex]\( P_2 \)[/tex] from the terms of [tex]\( P_1 \)[/tex]:
- For [tex]\( x^8 \)[/tex]:
- [tex]\( 9x^8 - 0x^8 = 9x^8 \)[/tex]
- For [tex]\( x^7 \)[/tex]:
- [tex]\( 8x^7 - 6x^7 = 2x^7 \)[/tex]
- For [tex]\( x \)[/tex]:
- [tex]\( 0x - 2x = -2x \)[/tex]
- For the constant term:
- [tex]\( 9 - 2 = 7 \)[/tex]
### Step 3: Write the resulting polynomial.
Putting it all together, the resulting polynomial after subtraction is:
[tex]\[ 9x^8 + 2x^7 - 2x + 7 \][/tex]
Therefore, the polynomial that represents the difference is option C:
[tex]\[ \boxed{9x^8 + 2x^7 - 2x + 7} \][/tex]
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