Mathematics
If (x - a) is a factor of x<sup>3</sup> - ax<sup>2</sup> + x + 5; the value of a is : 1. 2. 5 3. - 4. -5
Answer
By factor theorem,
If polynomial ƒ(x) is divided by its factor (x - a) then the remainder ƒ(a) = 0.
Since, x - a is a factor of x3 - ax2 + x + 5.
∴ On substituting x = a in x3 - ax2 + x + 5, remainder = 0.
∴ a3 - a(a)2 + a + 5 = 0
⇒ a3 - a3 + a + 5 = 0
⇒ a + 5 = 0
⇒ a = -5.
Hence, Option 4 is the correct option.
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