Factor 5x^2-2x-7

Problem

5*x2−2*x−7

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=−2 and c=−7

2. Multiply the leading coefficient a and the constant term c to find the product a*c

5⋅(−7)=−35

3. Find two numbers that multiply to −35 and add to the middle coefficient b=−2

−7⋅5=−35

−7+5=−2

4. Rewrite the middle term −2*x using the two numbers found in the previous step.

5*x2−7*x+5*x−7

5. Factor by grouping by splitting the expression into two pairs.

(5*x2−7*x)+(5*x−7)

6. Factor out the greatest common factor from each pair.

x*(5*x−7)+1*(5*x−7)

7. Factor out the common binomial factor (5*x−7)

(5*x−7)*(x+1)

Final Answer

5*x2−2*x−7=(5*x−7)*(x+1)

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