Question

find the square root of the following (x^2+3x+2)(x^2+4x+3)(x^2+5x+6)

Answer 1

Step-by-step explanation:

$(x^{2} +3x+2)(x^{2} +4x+3)(x^{2} +5x+6)\\\\\=(x^{2}+2x+x+2)(x^{2} +3x+x+3)(x^{2} +2x+3x+6)\\\\=[x(x+2)+1(x+2)][(x(x+3)+1(x+3)][x(x+2)+3(x+2)]\\\\=(x+1)(x+2)(x+1)(x+3)(x+3)(x+2)\\\\=(x+1)(x+1)(x+2)(x+2)(x+3)(x+3)\\\\=(x+1)^{2} (x+2)^{2} (x+3)^{2}\\\\=\sqrt{(x+1)^{2} (x+2)^{2} (x+3)^{2}} \\\\=(x+1)(x+2)(x+3)$

Using splitting the middle term :- In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term.

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