Question

which polynomial represents the difference below? $8x^8 + 9x^6 - x + 7 - (6x^8 + 4x^7 + 5)$ a. $14x^8 - 4x^7 - 9x^6 - x + 2$ b. $2x^0 + 5x^1 - x + 2$ c. $2x^8 - 4x^7 + 9x^6 - x + 2$ d. $2x^8 + 4x^7 + 9x^6 - x + 2$

Explanation:

Step1: Distribute the negative sign

We need to distribute the negative sign to each term inside the parentheses: \(8x^{8}+9x^{6}-x + 7-6x^{8}-4x^{7}-5\)

Step2: Combine like terms

• For the \(x^{8}\) terms: \(8x^{8}-6x^{8}=2x^{8}\)
• For the \(x^{7}\) terms: \(- 4x^{7}\) (since there is no other \(x^{7}\) term in the first polynomial)
• For the \(x^{6}\) terms: \(9x^{6}\) (since there is no other \(x^{6}\) term to combine with)
• For the \(x\) terms: \(-x\) (since there is no other \(x\) term to combine with)
• For the constant terms: \(7 - 5=2\)

Putting it all together, we get \(2x^{8}-4x^{7}+9x^{6}-x + 2\)

Answer:

C. \(2x^{8}-4x^{7}+9x^{6}-x + 2\)