Question

if f(x) = 4x⁴ + 3x - 4, then what is the remainder when f(x) is divided by x - 3?

Explanation:

Step1: Recall the Remainder Theorem

The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( x - a \), the remainder is \( f(a) \). Here, we are dividing by \( x - 3 \), so \( a = 3 \). We need to find \( f(3) \).

Step2: Substitute \( x = 3 \) into \( f(x) \)

Given \( f(x)=4x^{4}+3x - 4 \), substitute \( x = 3 \):

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Answer:

The remainder is \( 329 \).