Factor 3x^2+8x-3

Problem

3*x2+8*x−3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=8 and c=−3

2. Multiply the leading coefficient a and the constant term c to find the product a*c=3⋅(−3)=−9

3. Find two numbers that multiply to −9 and add to the middle coefficient b=8 These numbers are 9 and −1

4. Rewrite the middle term 8*x using the two numbers found: 3*x2+9*x−x−3

5. Factor by grouping the first two terms and the last two terms: (3*x2+9*x)+(−x−3)

6. Factor out the greatest common factor from each group: 3*x*(x+3)−1*(x+3)

7. Factor out the common binomial (x+3) to obtain the final factored form: (3*x−1)*(x+3)

Final Answer

3*x2+8*x−3=(3*x−1)*(x+3)

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