Factor 3x^2+7x-6

Problem

3*x2+7*x−6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=7 and c=−6

2. Calculate the product of a and c which is 3⋅−6=−18

3. Find two numbers that multiply to −18 and add up to the middle coefficient b=7 These numbers are 9 and −2

4. Rewrite the middle term 7*x using the two numbers found: 9*x−2*x

3*x2+9*x−2*x−6

5. Factor by grouping the first two terms and the last two terms.

3*x*(x+3)−2*(x+3)

6. Extract the common binomial factor (x+3) from the expression.

(3*x−2)*(x+3)

Final Answer

3*x2+7*x−6=(3*x−2)*(x+3)

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