Which Number to Use When Factoring

Question

In the example problem 4u2 + 12u = -5 I rearrange the equation to be 4u2 + 12u +5 = 0. The next step is to factor, but I would like to know when i should use (4u+1)(u+5)=0 instead of (2u+1)(2u+5)=0. Thanks.

Answer 1

When you properly arrange a quadratic equation so that the quadratic = 0, you then desire to factor it.

 

To check whether a particular factorization is correct, you multiply out to see if you get exactly the right quadratic product. Only one will be correct.

 

Multiplication of two binomials is done by the FOIL process; factoring is, then, the "unFOILing" process.

 

(2u+1)(2u+5)=0 is correct for this problem.