Need help factoring!?

Question

I need to factor 20n^2+34n+6

I know the answer but I really don't get how to do it. Can someone please explain to me how to do it step by step and help me get the answer?

Thanks

Answer 1

20n^2+34n+6

Factor out a common factor of 2

2(10n^2 + 17n + 3)

Multiply the first and last terms of the trinomial to get 30n^2. You need two n-terms that have a sum of 17n, but also have a product of 30n^2. 15n and 2n have a sum of 17n and a product of 30n^2.

2(10n^2 + 2n + 15n + 3)

Factor by grouping

2 [ 2n(5n + 1) + 3(5n + 1) ]

2 (2n + 3)(5n + 1)

Answer 2

The best way to go about factoring is to look at all of the numbers and try to see if there is a common factor that can be removed from the problem, in this case it's a two:
2(10n^2+17n+3).

Then you look at the number without a variable and figure out its factors. in this case you can only use 3 and 1. so those numbers have to go in the last to spots of you parenthesis:
2(__+3)(__+1).

Then since you need 10n^2, the first two numbers in the parenthesis either have to be 10 and 1 or 2 and 5.
Rationally looking at the equation, you can see that 10 and 1 will not work because you cannot get 17n you'll get a much bigger #. So you have to use 5 and 2. But you have to make sure that the 5 will multiply with the 3 so you will get a fifteen, b/c if not you will only end up with 11n. So the factors must be:
2(2n+3)(5n+1). if you don't like the two on the outside, you can multiply it into the first set of parenthesis and get (4n+6), giving you the original equation of 20n^2+34n+6

Answer 3

20n^2+34n+6
= 2(10n^2 + 17n + 3)
= 2(2n+3)(5n+1)

Answer 4

It factors into (4n^2+6)(5n^2+1). Set 4n^2+6=0 and 5n^2+1=0 and solve for the two solutions.

Answer 5

= 2.(10n² + 17n + 3)
= 2.(5n + 1).(2n + 3)

Answer 6

you would get

2(10n^2 +17n + 3 )

and tan te answer wld b

2 (5n+1)(2n+3)