Mathematics

Mathematics

Problem

Completely factorise x3+3x2−x−3x^{3}+3x^{2}-x-3 into linear factors. a) (x+3)(x+1)(x+1)(x+3)(x+1)(x+1) b) (x−3)(x+1)(x−1)(x-3)(x+1)(x-1) c) (x+3)(x+1)(x−1)(x+3)(x+1)(x-1) d) (x+3)(x2−3)(x+3)(x^{2}-3)
Intuitive explanation

The key is to recognize that this cubic has a hidden grouping structure. Notice you can pair the terms strategically: group the first two and last two terms separately, factor out the common factor from each pair, and you'll discover a repeated binomial factor that lets you factor further. This turns a tricky cubic into a product of three linear factors.

Intuitive explanation

The key is to recognize that this cubic has a hidden grouping structure. Notice you can pair the terms strategically: group the first two and last two terms separately, factor out the common factor from each pair, and you'll discover a repeated binomial factor that lets you factor further. This turns a tricky cubic into a product of three linear factors.

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