Answer :
To solve for the polynomial representing the difference, we need to subtract the polynomials given in the problem:
The initial expression is:
[tex]\[ x^7 - 3x + 10 - (9x^8 + 4x) \][/tex]
To subtract these, we'll distribute the negative sign in front of the second polynomial across its terms:
[tex]\[ = x^7 - 3x + 10 - 9x^8 - 4x \][/tex]
Next, rearrange the terms to combine like terms:
[tex]\[ = -9x^8 + x^7 - 3x - 4x + 10 \][/tex]
Now, combine the like terms ([tex]\(-3x\)[/tex] and [tex]\(-4x\)[/tex]):
[tex]\[ = -9x^8 + x^7 - 7x + 10 \][/tex]
Therefore, the polynomial that represents the difference is:
[tex]\[ -9x^8 + x^7 - 7x + 10 \][/tex]
So, the correct answer is:
C. [tex]\(-9x^8 + x^7 - 7x + 10\)[/tex]
The initial expression is:
[tex]\[ x^7 - 3x + 10 - (9x^8 + 4x) \][/tex]
To subtract these, we'll distribute the negative sign in front of the second polynomial across its terms:
[tex]\[ = x^7 - 3x + 10 - 9x^8 - 4x \][/tex]
Next, rearrange the terms to combine like terms:
[tex]\[ = -9x^8 + x^7 - 3x - 4x + 10 \][/tex]
Now, combine the like terms ([tex]\(-3x\)[/tex] and [tex]\(-4x\)[/tex]):
[tex]\[ = -9x^8 + x^7 - 7x + 10 \][/tex]
Therefore, the polynomial that represents the difference is:
[tex]\[ -9x^8 + x^7 - 7x + 10 \][/tex]
So, the correct answer is:
C. [tex]\(-9x^8 + x^7 - 7x + 10\)[/tex]
