Question

question 5 (multiple choice worth 5 points) (03.01r) what is the remainder when $(2x^3 + 4x^2 - 32x + 18) \div (x + 3)$? 2 12 96 110

Explanation:

Step1: Recall Remainder Theorem

The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( (x - a) \), the remainder is \( f(a) \). Here, we divide by \( (x + 3)=(x - (-3)) \), so \( a=-3 \).

Step2: Define the polynomial

Let \( f(x)=2x^{3}+4x^{2}-32x + 18 \).

Step3: Substitute \( x=-3 \) into \( f(x) \)

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Answer:

96