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Question
Using the Remainder and Factor Theorem, factorise the following polynomial: x3 + 10x2 – 37x + 26.
Solution
f(x) = x3 + 10x2 – 37x + 26
f(1) = (1)3 + 10(1)2 – 37(1) + 26
= 1 + 10 – 37 + 26 = 0
x = 1
`x – 1")"overline(x^3 + 10x^3 – 37x + 26)("x^2 + 11x – 26`
x3 – x2
– +
11x2 – 37x
11x2 – 11x
– +
–26x + 26
–26x + 26
+ –
0
x – 1 is factor of f(x)
∴ f(x) = (x – 1)(x2 + 11x – 26)
= (x – 1)(x2 + 13x – 2x – 26)
= (x – 1)[x(x + 13) – 2(x + 13)]
= (x – 1)[(x – 2)(x + 13)].
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