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 the two numbers found: 5*x2−5*x+3*x−3

5. Factor by grouping the first two terms and the last two terms: 5*x*(x−1)+3*(x−1)

6. Factor out the common binomial factor (x−1)

Final Answer

5*x2−2*x−3=(5*x+3)*(x−1)

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