Factor 6x^2+11x-35

Problem

6*x2+11*x−35

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=6 b=11 and c=−35

2. Calculate the product a*c by multiplying 6 and −35

a*c=6⋅(−35)=−210

3. Find two numbers that multiply to −210 and add to the middle coefficient b=11 These numbers are 21 and −10

4. Rewrite the middle term 11*x using the two numbers found in the previous step.

6*x2+21*x−10*x−35

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

3*x*(2*x+7)−5*(2*x+7)

6. Factor out the common binomial factor (2*x+7)

(3*x−5)*(2*x+7)

Final Answer

6*x2+11*x−35=(3*x−5)*(2*x+7)

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