Factor 3x^2+26x+35

Problem

3*x2+26*x+35

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=26 and c=35

2. Calculate the product a*c by multiplying 3 and 35

a*c=3⋅35=105

3. Find two numbers that multiply to 105 and add up to the middle coefficient b=26

21⋅5=105

21+5=26

4. Rewrite the middle term 26*x using the two numbers found in the previous step.

3*x2+21*x+5*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*(x+7)+5*(x+7)

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

(3*x+5)*(x+7)

Final Answer

3*x2+26*x+35=(3*x+5)*(x+7)

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