Factor x^3+5x^2+6x

Problem

x3+5*x2+6*x

Solution

1. Identify the greatest common factor of all three terms, which is x

2. Factor out the x from the expression.

x*(x2+5*x+6)

3. Identify two numbers that multiply to 6 and add to 5 to factor the quadratic trinomial x2+5*x+6

4. Determine that the numbers are 2 and 3 since 2⋅3=6 and 2 + 3 = 5$.

5. Rewrite the quadratic part as a product of two binomials.

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

Final Answer

x3+5*x2+6*x=x*(x+2)*(x+3)

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