Factor 9x^3+6x^2-3x

Problem

9*x3+6*x2−3*x

Solution

1. Identify the greatest common factor (GCF) of all three terms in the expression.

2. Determine that the GCF of the coefficients 9 6 and −3 is 3

3. Determine that the GCF of the variables x3 x2 and x is x

4. Factor out the GCF, which is 3*x from each term.

3*x*(3*x2+2*x−1)

5. Factor the quadratic expression 3*x2+2*x−1 inside the parentheses by finding two numbers that multiply to −3 and add to 2

6. Rewrite the middle term 2*x as 3*x−x and factor by grouping.

3*x2+3*x−x−1

3*x*(x+1)−1*(x+1)

(3*x−1)*(x+1)

7. Combine all factors into the final expression.

Final Answer

9*x3+6*x2−3*x=3*x*(3*x−1)*(x+1)

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