Question

6d^2–9d–15 How do i factor this out.

Answer 1

the given expression
`(6d^2 - 9d- 15)` is factored as (d+1)(2 d-5)

Explanation:

Here, the given expression is:

`6d^2 - 9d- 15= 0`

Now, simplifying the given expression,we get:

`6d^2 - 9d- 15= 0 \\\implies 3(2d^2 - 3d- 5) = 0\\\implies 2d^2 - 3d- 5 = 0`

Now, we need to split the middle term -3 in such a way, that on addition it given -3 and on multiplication it given -10.

`2d^2 - 3d- 5 = 0\\\implies 2d^2 + 2d- 5d - 5 = 0\\\implies 2d(d+1) -5(d+1) = 0\\\implies (d+1)(2d-5) = 0`

So, either(d+1) = 0 OR (2d-5) = 0

⇒
`(6d^2 - 9d- 15) = (d+1)(2d-5)`

Hence the given expression
`(6d^2 - 9d- 15)` is factored as (d+1)(2 d-5) = 0