Question

What is the factored form of the expression. (2n^2 + 5n + 3) (4n - 5)

Answer 1

So firstly, the factor (4n - 5) cannot be further factored, so we will be focusing on 2n² + 5n + 3.

So for this, we will be factoring by grouping. Firstly, what two terms have a product of 6n² and a sum of 5n? That would be 2n and 3n. Replace 5n with 2n + 3n:

`(2n^2 + 2n + 3n + 3)(4n - 5)`

Next, factor 2n² + 2n and 3n + 3 separately. Make sure that they have the same quantity on the inside of the parentheses:

`(2n(n+1)+3(n+1))(4n-5)`

Now we can rewrite this expression as
`(2n+3)(n+1)(4n-5)` , which is your final answer.