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Question
Factorise : x3 + 13x2 + 32x + 20
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Solution
Let us split the middle terms as shown below:
x3 + 13x2 + 32x + 20 = x3 + 10x2 + 3x2 + 30x + 2x + 20
= x2(x + 10) + 3x(x + 10) + 2(x + 10)
= (x + 10) (x2 + 3x + 2)
= (x + 10) (x2 + 2x + x + 2)
= (x + 10) [x(x + 2) + (x + 2)]
= (x + 10)(x + 2) (x + 1)
Hence, x3 + 13x2 + 32x + 20 = (x + 1) (x + 2)(x + 10).
x3 + 13x2 + 32x + 20 = x3 + 10x2 + 3x2 + 30x + 2x + 20
= x2(x + 10) + 3x(x + 10) + 2(x + 10)
= (x + 10) (x2 + 3x + 2)
= (x + 10) (x2 + 2x + x + 2)
= (x + 10) [x(x + 2) + (x + 2)]
= (x + 10)(x + 2) (x + 1)
Hence, x3 + 13x2 + 32x + 20 = (x + 1) (x + 2)(x + 10).
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