Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. the remainder after dividing $x^4 + 3x^3 - 8x^2 + 5x - 9$ by $x + 5$ is \boxed{}.

Explanation:

Step1: Recall Remainder Theorem

The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( x - a \), the remainder is \( f(a) \). For \( x + 5 \), we can write it as \( x - (-5) \), so \( a=-5 \).

Step2: Substitute \( x = -5 \) into \( f(x) \)

Let \( f(x)=x^{4}+3x^{3}-8x^{2}+5x - 9 \). Substitute \( x=-5 \):

$$
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$$

Answer:

16