Question

factor completely
2x^2-5x-12

Answer 1

You can try factopring by guessing.

\(2x^2 - 5x - 12\)

The \(2x^2\) term comes from 2x * x, so you start with:

\(= (2x~~~~)(x~~~~~)\)

Answer 2

Now you need two numbers that multiply to -12.
Can you list all the possibilities?

Answer 3

yes 6,2,3,4

Answer 4

Good, but remember to include 1 and 12 also.
By all the possibilities I mean all pairs of numbers that multiply to -12.
Here they are:
-1, 12
-12, 1
-2, 6
-6, 2
-4, 3
-3, 4
Each of those pairs has a product of -12.

Answer 5

Now we need to place them in the parentheses in a way that when you multiply the two binomials together, you get the correct middle term, -5x.

Answer 6

ok so neither adds to make -5

Answer 7

\(= (2x+\square )(x+\triangle)\)
One number goes where the square is and the other number goes where the triangle is.
The way we know which two numbers we use and where we put them is by multiplying out the OI of FOIL and adding them up and making sure we get -5x.

Answer 8

ok so they do not make -5x

Answer 9

Let's try -4, 3, in that order:
\((2x -4)(x + 3)\)
OI: 6x - 4x = 2x which is not -5x, so this is not it.

Let's try 3, -4:
\((2x + 3)(x - 4)\)
OI: -8x + 3x = -5x which is what we needed, so this is correct.

\(2x^2 - 5x - 12 = (2x + 3)(x - 4) \)

Answer 10

ok now i get it. Thanks for your help.

Answer 11

Keep in mind that factoring a trinomial is the opposite of multiplying two binomials together. To multiply binomials together, you can use FOIL, so you can use FOIL to check if you factored the trinomial correclty.

Answer 12

You're welcome.