Answer:
d. -6
Explanation:
By the remainder theorem, we get that:
[tex]f(x)=(x+1)\cdot q(x)+r[/tex]
Where q(x) is another polynomial and r is the remainder.
To eliminate the value of q(x), we will replace x by -1 to get:
[tex]\begin{gathered} f(-1)=(-1+1)\cdot q(-1)+r \\ f(-1)=0\cdot q(x)+r \\ f(-1)=r \end{gathered}[/tex]
But f(x) = x^(88) + 5x - 2, so f(-1) will be equal to:
[tex]\begin{gathered} f(x)=x^{88}+5x-2 \\ f(-1)=(-1)^{88}+5(-1)-2 \\ f(-1)=1-5-2 \\ f(-1)=-6_{} \end{gathered}[/tex]
Therefore, if f(-1) = -6 and f(-1) = r, we get that
r = -6
So, the remainder is d. -6
