Question

which polynomial represents the difference below?
$(9x^8 + 8x^7 + 9) - (6x^7 + 2x + 2)$

a. $9x^8 + 14x^7 + 2x + 7$

b. $9x^{15} + 3x^7 + 7$

c. $9x^8 + 2x^7 - 2x + 7$

d. $3x^8 + 2x^7 - 2x + 7$

Explanation:

Step1: Distribute the negative sign

To subtract the second polynomial from the first, we distribute the negative sign to each term in the second polynomial:
$$(9x^8 + 8x^7 + 9) - (6x^7 + 2x + 2) = 9x^8 + 8x^7 + 9 - 6x^7 - 2x - 2$$

Step2: Combine like terms

• For the \(x^8\) term: There is only \(9x^8\), so it remains \(9x^8\).
• For the \(x^7\) terms: \(8x^7 - 6x^7 = 2x^7\)
• For the \(x\) term: There is only \(-2x\), so it remains \(-2x\)
• For the constant terms: \(9 - 2 = 7\)

Putting it all together, we get:
$$9x^8 + 2x^7 - 2x + 7$$

Answer:

C. \(9x^8 + 2x^7 - 2x + 7\)