Question:
If \( (x - 2) \) is a factor of \( x^3 - 4x^2 + ax + 8 \), find the value of \( a \):
If \( (x - 2) \) is a factor of \( x^3 - 4x^2 + ax + 8 \), find the value of \( a \):
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Use the Factor Theorem: if \( (x - r) \) is a factor of \( f(x) \), then \( f(r) = 0 \).
Updated On: Mar 18, 2026
- 0
- 2
- 3
- 5
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The Correct Option is A
Solution and Explanation
Given: The polynomial is:f(x) = x³ - 4x² + ax + 8
and it is given that (x - 2) is a factor of the polynomial.
Step 1: Recall the Factor Theorem
Factor Theorem states that if (x - c) is a factor of a polynomial f(x), then f(c) = 0.
Step 2: Apply the Factor Theorem
Since (x - 2) is a factor, we substitute x = 2 into the polynomial and set the result equal to zero:
f(2) = (2)³ - 4(2)² + a(2) + 8 = 8 - 16 + 2a + 8
Step 3: Simplify the expression
Combine like terms: f(2) = (8 - 16 + 8) + 2a = 0 + 2a
Step 4: Solve for 'a'
2a = 0⇒ a = 0
Final Answer: a = 0
Hence, the correct option is Option (1): 0
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