Factor x^3+2x^2+3x+6

Problem

x^3+2*x^2+3*x+6

Solution

1. Group the terms into two pairs to prepare for factoring by grouping.

(x^3+2*x^2)+(3*x+6)

2. Factor out the greatest common factor from the first pair, which is x^2

x^2*(x+2)+(3*x+6)

3. Factor out the greatest common factor from the second pair, which is 3

x^2*(x+2)+3*(x+2)

4. Factor out the common binomial (x+2) from the entire expression.

(x^2+3)*(x+2)

Final Answer

x^3+2*x^2+3*x+6=(x^2+3)*(x+2)

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