factor the trinomial 3x2-2x-8 write each factor as a polynomial in descending order

Question

mathstudent55 · Answer

You have a trinomial of the form
$ax^2 + bx + c$

mathstudent55 · Answer

The first step in factoring is to see if there is a common factor for all terms.
Can you check that?

mathstudent55 · Answer

If you just look at the coefficients (the numbers), you notice that 3, -2, and -8 have no common factor, so there is no common factor for all three terms that can be factored out.

mathstudent55 · Answer

We have a trinomial of the form $ax^2 + bx + c$ in which $ a \ne 1$. In other words, $x^2$ is not multiplied by 1, but by some other number.

anonymous · Answer

so its (x-2) (3x-2)

mathstudent55 · Answer

No. (Try L of FOIL and you'll see it doesn't work.)

For this kind of factoring, we use the ac method.
Your trinomial has a = 3, b = -2, and c = -8.

First we multiply together ac: 3(-8) = -24
Now we look for 2 numbers whose product is -24 and which add to b, -2.
Can you come up with tweo numbers that add to -2 and multiply to -24?

anonymous · Answer

-6,4

mathstudent55 · Answer

Great.
Now we break up the middle term into two terms using those two numbers.

$3x^2 - 6x + 4x - 8 $

Ok?

mathstudent55 · Answer

Now we factor by parts. That means take a common factor out of the first two terms, and take a common factor out of the last two terms.

mathstudent55 · Answer

$3x (x - 2) + 4(x - 2) $

Finally, notice that the term x - 2 is now a common term, so you can factor x - 2 out giving you the answer:

$ (x - 2) (3x + 4) $

anonymous · Answer

ok yeah i got the right answer then thanks dude

mathstudent55 · Answer

wlcm