Factor 7a^2+53a+28

Problem

7*a2+53*a+28

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=7 b=53 and c=28

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

7×28=196

3. Find two numbers that multiply to 196 and add up to the middle coefficient b=53

4×49=196

4+49=53

4. Rewrite the middle term 53*a using the two numbers found in the previous step.

7*a2+49*a+4*a+28

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

7*a*(a+7)+4*(a+7)

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

(7*a+4)*(a+7)

Final Answer

7*a2+53*a+28=(7*a+4)*(a+7)

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