Factor 5x^2+2x-3

Problem

5*x2+2*x−3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=2 and c=−3

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

3. Determine the pair of numbers, which are 5 and −3 since 5⋅(−3)=−15 and 5 + (-3) = 2$.

4. Rewrite the middle term 2*x using these two numbers as 5*x−3*x

5*x2+5*x−3*x−3

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

5*x*(x+1)−3*(x+1)

6. Factor out the common binomial (x+1)

(5*x−3)*(x+1)

Final Answer

5*x2+2*x−3=(5*x−3)*(x+1)

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