Question

which polynomial represents the difference below?
$5x^7 - 8x + 2 - (7x^8 + 3x)$
a. $-7x^8 + 5x^7 - 11x + 2$
b. $2x^1 + -5x - 2$
c. $-7x^8 + 5x^7 - 5x + 2$
d. $12x^{15} + 11x + 2$

Explanation:

Step1: Distribute the negative sign

To simplify \(5x^{7}-8x + 2-(7x^{8}+3x)\), we first distribute the negative sign to each term inside the parentheses. This gives us \(5x^{7}-8x + 2-7x^{8}-3x\).

Step2: Combine like terms

Next, we combine the like terms. The \(x\)-terms are \(-8x\) and \(-3x\). Combining these, we get \(-8x-3x=-11x\). The other terms remain as they are: \(5x^{7}\), \(-7x^{8}\), and \(2\). Putting it all together, we have \(-7x^{8}+5x^{7}-11x + 2\).

Answer:

A. \(-7x^{8}+5x^{7}-11x + 2\)