Factor 6x^2+7x-3

Problem

6*x2+7*x−3

Solution

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

2. Find two numbers that multiply to a⋅c=6⋅−3=−18 and add to b=7

3. Determine the pair of numbers, which are 9 and −2 since 9⋅−2=−18 and 9 + (-2) = 7$.

4. Rewrite the middle term 7*x using these two numbers as 9*x−2*x

6*x2+9*x−2*x−3

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

3*x*(2*x+3)−1*(2*x+3)

6. Factor out the common binomial (2*x+3)

(3*x−1)*(2*x+3)

Final Answer

6*x2+7*x−3=(3*x−1)*(2*x+3)

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