Question

How do you factor `2x^2+19x+24`?

Answer 1

`(2x+3)(x+8)`

Explanation:

When you factor a quadratic equation of the form `ax^2+bx+c`, you must find two numbers which, when multiplied, give `ac`, and when added, give `b`.

First let us compute `ac`.
`2*24=48`

Therefore, the two numbers add up to `19`, and multiply to give `48`.

List out the factors of `48`. I'm going to list them in pairs (each pair will multiply to give `48`, for example, `4` and `12`). You should be able to run through the factors in your head; listing out takes a lot of time.

`(1,48), (2,24), (3,16), (4, 12), (6,8)`.

Now, what of the above pairs add up to `19`? `3` and `16` do.

So now we have the equation, `2x^2+19x+24`

`=2x^2+16x+3x+24` (the factor pair)

`=2x(x+8)+3(x+8)`

`=(2x+3)(x+8)`

Factored.