Question

How do i factor 4x squared+28x+48

Answer 1

Hey there!

For this, the easiest way to do this is guess+check with some logic behind it. First, we see the equation:

`4x^2+28x+48\\`

Now to do this, first, we want to see what the ways to break up
`4x^2` are. We can make it
`4x\cdot x` or
`2x\cdot 2x`. We also want to see what ways we can break up 48:
`1\cdot 48, 2\cdot 24, 3\cdot 16, 4\cdot 12, 6\cdot 8\\`.

From this, we want it so we can multiply these pairs by each other and add them up to equal 28. We already can cross out the first two ways to break up 48 as 48 is greater than 28 already, and though 24 is less, if we were to multiply that by x we would get 24x, and for the remaining 2 it would become 8x (as remember x and 4x are paired, meaning you have to multiply 2 by the other half of the pair, 4x). Adding these gets 32x, which is greater than 28x.

We are left with:

`4x\cdot x, 2x\cdot 2x`

`3\cdot 16, 4\cdot 12, 6\cdot 8`

Now, actually, funny thing is all of these happen to work. If you were to multiply 3 by 4x, and 16 by x, you would get 12x+16x=28x. If you were to multiply 4 by 4x, and x by 12, you would also get 12x+16x=28x. Finally, if you were to multiply 6 by 2x and 8 by 2x, you would get 12x+16x=28x. So really here, you can take your pick. let's use 6*8. Writing this out, we get:

(2x+6)(2x+8)

Hope this helps! Sorry that this explanation was actually quite a bad one, if you have any additional questions just ask me.