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Question
Factorise x3 + 6x2 + 11x + 6 completely using factor theorem.
Solution
Let f(x) = x3 + 6x2 + 11x + 6
For x = –1
f(–1) = (–1)3 + 6(–1)2 + 11(–1) + 6
= –1 + 6 – 11 + 6
= 12 – 12
= 0
Hence, (x + 1) is a factor of f(x).
x2 + 5x + 6
`x + 1")"overline(x^3 + 6x^2 + 11x + 6)`
x3 + x2
5x2 + 11x
5x2 + 5x
6x + 6
6x + 6
0
∴ x3 + 6x2 + 11x + 6 = (x + 1)(x2 + 5x + 6)
= (x + 1)(x2 + 2x + 3x + 6)
= (x + 1)[x(x + 2) + 3(x + 2)]
= (x + 1)(x + 2)(x + 3)
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