Question
Download Solution PDFWhat must be added to (x3 - 3x2 + 4x - 75) to obtain a polynomial that is exactly divisible by (x - 5)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
What must be added to (x3 - 3x2 + 4x - 75) to obtain a polynomial that is exactly divisible by (x - 5)?
Formula Used:
If a polynomial f(x) is exactly divisible by (x - a), then f(a) = 0.
Calculation:
Let f(x) = x3 - 3x2 + 4x - 75 + k
Since f(x) is divisible by (x - 5), we have f(5) = 0.
f(5) = 53 - 3(5)2 + 4(5) - 75 + k
⇒ 125 - 75 + 20 - 75 + k = 0
⇒ -5 + k = 0
⇒ k = 5
∴ The correct answer is option (4).
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