Question

What is the remainder of f(x)=x^3+x^2-9x+23 When divided by binomial X +4

Answer 1

The remainder is 11.

Explanation:

We are given the polynomial:

`f(x) = x^3 + x^2 - 9x + 23`

And we want to find its remainder when the polynomial is divided by:

`x + 4`

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):

`\displaystyle \begin{aligned}f(-4) &= (-4)^3 + (-4)^2 - 9(-4) + 23 \\ &= 11 \end{aligned}`

In conclusion, the remainder of the operation is 11.