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Question
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
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Solution
f(x) = 2x3 + x2 – 13x + 6
Factors of constant term 6 are ±1, ±2, ±3, ±6.
By hit and trail, putting x = 2, f(2) = 2(2)3 + 22 – 13 (2) + 6 = 0,
Hence (x – 2) is a factor of f(x) using factor theorem
So f(x)= 2x2 (x – 2) + 5x (x – 2) – 3 (x – 2)
= (x – 2) (2x2 + 5x – 3)
= (x – 2) [2x2 + 6x – x – 3]
= (x – 2) [2x (x + 3) – (x + 3)]
= (x – 2) (x + 3) (2x – 1)
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