Question

Factor this trinomial 4x^2-6x-10 If you can please try to show me how to do it.

Answer 1

`=2(2x-5)(x+1)`

Explanation:

So we have the trinomial:

`4x^2-6x-10`

First, factor out a 2:

`=2(2x^2-3x-5)`

Now, factor within the parentheses.

To do so, we want to find two numbers. When multiplied, these two numbers must equal (a)(c) and when added, they must equal b

(a)(c) is 2(-5) or -10 and b is -3. So, we want two numbers that when multiplied together gives -10 and when added gives -3.

-5 and 2 works. Therefore:

`=2(2x^2-3x-5)`

Replace -3x with 2x and -5x:

`=2(2x^2+2x-5x-5)`

Factor out a 2x for the first two terms. And factor out a negative 5 for the remaining two:

`=2(2x(x+1)-5(x+1))`

Grouping:

`=2(2x-5)(x+1)`

And we're done!