What must be added to (x3 - 3x2 + 4x - 75) to obtain a polynomial that is exactly divisible by (x - 5)?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 5.
Let the number to be added to the equation be a.
f(x) = x3 - 3x2 + 4x - 75 + a
According to the given question,
When a polynomial is completely divided by (x - k) then, f(k) = 0.
Now, given polynomial is completely divisible by (x - 5), f(5) = 0
⇒ 53 - 3(5)2 + 4(5) - 75 + a = 0
⇒ 125 - 75 + 20 - 75 + a = 0
⇒ 145 - 150 + a = 0
⇒ a - 5 = 0
⇒ a = 5
Hence the number to added to the polynomial is 5.