Find, by factoring, the zeros of the function 𝑓 of 𝑥 equals 12𝑥 squared minus
14𝑥 minus six.
So in order to find these zeros, we need to set it equal to zero. And now we
can take out a greatest common factor of two.
So focusing on the polynomial on the inside, we’re
going to use a method that we call slip and slide. So I’m going to slip the six to the back,
and we will take six times negative three.
And now we need to come up with two numbers that
multiply to be negative 18 and add to be negative seven. So here are a few pairs that
multiply to be negative 18. So the pair that adds to be negative seven would be negative
nine and two.
Now our next step is to slide the six that we brought to the back underneath the
nine and the two. And now we simplify; that’s how we get our slip and slide method.
However, we don’t wanna leave our factors in the terms of fractions, so the two that’s left on the bottom
we will move it up with the 𝑥 and the same with the three.
Now when solving for zeros, you wouldn’t necessarily have to do this step. You could leave it as 𝑥 minus three-halves and 𝑥 plus
one-third and solve. It would actually be easier, but most of the time, you do see it in this
form of two 𝑥 minus three and three 𝑥 plus one. And also don’t forget to bring down your two.
So now we set every factor equal to zero. Now as we said we’re solving; it will be easier to use
what’s underlined. Now setting two equal to zero, our greatest common factor doesn’t do anything;
that’s not even true, so you can just mark it out.
Now we would add three-halves to the right and we would subtract one-third to the right. So three-halves and negative one-third would be
the zeros of this function.