Factor 9x^2+7x-56

Problem

9*x2+7*x−56

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=9 b=7 and c=−56

2. Calculate the product of a and c which is 9×−56=−504

3. Search for two integers that multiply to −504 and add to the middle coefficient b=7

4. Test factors of −504

21×−24=−504

21+(−24)=−3

24×−21=−504

24+(−21)=3

28×−18=−504

28+(−18)=10

5. Determine if the expression is factorable over the integers. Since no two integer factors of −504 sum to 7 the quadratic cannot be factored using the grouping method with integers.

6. Check the discriminant D=b2−4*a*c to see if the roots are rational.

D=7−4*(9)*(−56)

D=49+2016

D=2065

7. Conclude that since 2065 is not a perfect square, the expression is irreducible over the integers.

Final Answer

9*x2+7*x−56=9*x2+7*x−56

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