Question

question
given ( f(x) = 2x^3 - 6x + k ), and the remainder when ( f(x) ) is divided by ( x - 2 ) is 21, then what is the value of ( k )?
answer attempt 1 out of 2
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Explanation:

Step1: Apply Remainder Theorem

The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( x - a \), the remainder is \( f(a) \). Here, \( a = 2 \) (since we divide by \( x - 2 \)) and the remainder is 21. So we need to find \( f(2) \) and set it equal to 21.

Step2: Substitute \( x = 2 \) into \( f(x) \)

Given \( f(x) = 2x^3 - 6x + k \), substitute \( x = 2 \):

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Step3: Solve for \( k \)

We know \( f(2) = 21 \) (from the remainder). So:

$$ 4 + k = 21 $$

Subtract 4 from both sides:

$$ k = 21 - 4 = 17 $$

Answer:

17