Question

if $f(x) = 2x^2 + 3x - 5$, then what is the remainder when $f(x)$ is divided by $x - 4$?

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 \( x - 4 \), so \( a = 4 \).

Step2: Substitute \( x = 4 \) into \( f(x) \)

We have \( f(x)=2x^{2}+3x - 5 \). Substitute \( x = 4 \):

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Answer:

The remainder is \( 39 \).