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Question
Using the Remainder and Factor Theorem, factorise the following polynomial:
`x^3 + 10x^2 - 37x + 26`
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Solution
`f(x) = x^3 + 10x^2 - 37x + 26`
For x = 1
`f(1) = (1)^2 + 10(1)^2 - 37(1) + 26`
= 1 + 10 - 37 + 26
= 0
=> (x - 1) is a factor of `x^3 + 10x^2 - 37x + 26`
Now
Thus by factor theorem
`=> x^3 + 10x^2 - 37x + 26 = (x - 1)(x^2 + 11x - 26)`
`= (x - 1) (x^2 + 13x - 2x - 26)`
`= (x - 1)(x(x + 13) - 2(x + 13))`
`=> x^3 + 10x^2 - 37x + 26 = (x - 1)(x + 13)(x - 2)`
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