Mathematics

Mathematics

Problem

Which of the following gives the complete factorisation of 3x2+11x+63x^{2}+11x+6? a) (3x−2)(x+3)(3x-2)(x+3) b) (x+2)(3x+3)(x+2)(3x+3) c) (3x+2)(x+3)(3x+2)(x+3) d) (3x−2)(x−3)(3x-2)(x-3)
Intuitive explanation

The key is recognizing this as a quadratic trinomial where the leading coefficient isn't 1. You need two numbers that multiply to 3×6=183 \times 6 = 18 and add to 1111—that's your "AC method" shortcut. Once you find them, use those numbers to split the middle term and factor by grouping, which will reveal the two binomial factors hiding inside.

Intuitive explanation

The key is recognizing this as a quadratic trinomial where the leading coefficient isn't 1. You need two numbers that multiply to 3×6=183 \times 6 = 18 and add to 1111—that's your "AC method" shortcut. Once you find them, use those numbers to split the middle term and factor by grouping, which will reveal the two binomial factors hiding inside.

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