Question

How do you factor `2d^2-7d-15`?

Answer 1

`(2d+3)(d-5)`.

Explanation:

This may be factorized as a trinomial to obtain the factors

`(2d+3)(d-5)`.

To obtain this you look at the coefficient of the first term, 2, and see what its factors are. There is only 1 option, `1xx2`.

Then look at the coefficient of the last term, 15, and there are a 2 options here namely :
`1xx15 or 3xx5`.

You now need to combine the options such that the sum of the factors when cross-multiplied give you the middle term of `-7`.

The only option is `((2,3),(1,-5))` since `1xx3-2xx-5=-7`

and so therefore the factors are the rows of the matrix shown.

Answer 2

`(2d+3)(d−5)`

Explanation:

Factor `2d^2`−`7d`−`15` ?

To factor a quadratic function with a leading coefficient greater than 1, do the following steps:

• Multiply the leading coefficient and the constant:

`2 *`-`15 =`-`30`

• What two numbers would multiply to give you -`30` and add to give you -`7` ?

`3 *`-`10 =`-`30`
`3 +`-`10 =`-`7`

So, +`3` & -`7`.

• Since we multiplied the constant by 2, divide the numbers you got above by 2:

`+3/2 & -10/2`

`-10/2 =`-`5` so, one of the factors is `(d-5)`
but `+3/2` leaves you with an improper fraction, right? (Yes.)
So, instead of `(d+3)` we're going to have `(2d+3)`.

• Final factors:

`(2d+3)(d-5)`