Mathematics
When 2x3 + 5x2 - 2x + 8 is divided by (x - a) the remainder is 2a3 + 5a2. Find the value of a.
Factorisation
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Answer
By remainder theorem,
If f(x), a polynomial in x, is divided by (x - a), the remainder = f(a).
∴ On dividing 2x3 + 5x2 - 2x + 8 by (x - a)
Remainder = 2a3 + 5a2 - 2a + 8
Given, remainder = 2a3 + 5a2.
∴ 2a3 + 5a2 - 2a + 8 = 2a3 + 5a2
⇒ -2a + 8 = 0
⇒ 2a = 8
⇒ a = 4.
Hence, a = 4.
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