Solve by factoring:

5x^2 + 19x + 12 = 0

When solving polynomial equations, first set the equation

equal to zero, then check for a Greatest Common Factor.

Since there is no greatest common factor, this will make life a

little bit more difficult because we will have to factor the trinomial.

First, find all possible factors for constant term.

I have listed these in red below.

Make sure to reverse the factors since in each binomial,

the first term is different so we need to reverse the factors.

The factors of 5x² will just be 5x and z.

After finding factors for the constant and the leading

coefficient for your trinomial, we can eliminate some factors.

If you have an odd coefficient on the middle term,

you can eliminate any pairs of even factors.

So the group I crossed out in purple below will be eliminated.

Another strategy is to use factors a little closer together.

So I would go with the 4 and 3 group.

Surely enough, our trinomial does factor with the 4 and 3.

Now set the factored trinomial equal to 0.

Then use zero product property and you have your answer.

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!