Factor 5x^2-34x-7

Problem

5*x2−34*x−7

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=5 b=−34 and c=−7

2. Calculate the product of a and c which is 5×−7=−35

3. Find two numbers that multiply to −35 and add to the middle coefficient b=−34 These numbers are −35 and 1

4. Rewrite the middle term −34*x using the two numbers found: −35*x+1*x

5*x2−35*x+x−7

5. Factor by grouping the first two terms and the last two terms.

5*x*(x−7)+1*(x−7)

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

(5*x+1)*(x−7)

Final Answer

5*x2−34*x−7=(5*x+1)*(x−7)

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