Factor 5x^2+14x-3

Problem

5*x2+14*x−3

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=5 b=14 and c=−3

2. Find two numbers that multiply to a⋅c=5⋅(−3)=−15 and add to b=14

3. Determine that the two numbers are 15 and −1

4. Rewrite the middle term 14*x using these two numbers as 15*x−x

5. Group the terms into two pairs: (5*x2+15*x)+(−x−3)

6. Factor out the greatest common factor from each pair: 5*x*(x+3)−1*(x+3)

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

Final Answer

5*x2+14*x−3=(5*x−1)*(x+3)

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