math help for precalculus

Question

solve the following polynomial equation algebraically. Answer in exact form. 6x^3 + 7x^2 - 5x = 0

Answer 1

We solve polynomial equations by making sure they are = 0, then factoring.

In this example, we can factor out x immediately (which will yield x= 0 as one of three solutions.

x (6x² + 7x - 5) = 0

Now we can factor the remaining quadratic (a quick check of the discriminant, 169, reveals it is factorable):

x (2x - 1)(3x + 5) = 0. Finally, setting each factor = 0 and solving, gives ...

x=0 or x=1/2 or x=-5/3