Answer:
The remainder is 11.
Step-by-step explanation:
We are given the polynomial:
[tex]f(x) = x^3 + x^2 - 9x + 23[/tex]
And we want to find its remainder when the polynomial is divided by:
[tex]x + 4[/tex]
We can use the Polynomial Remainder Theorem. According to the PRT, if we divide a polynomial P(x) by a binomial in the form (x - a), the remainder will be given by P(a).
In this case, our binomial is (x + 4) or (x - (-4)). Hence, a = -4.
Then the remainder will be f(-4):
[tex]\displaystyle \begin{aligned}f(-4) &= (-4)^3 + (-4)^2 - 9(-4) + 23 \\ &= 11 \end{aligned}[/tex]
In conclusion, the remainder of the operation is 11.
