Math question...?

Question

Anyone know anything about factoring trinomials?

Okay factor completely??

1) 36 x^2 + 60 +9

2) 24x^2 - 46x + 10

Answer 1

I'm not going to do your work for you. However, to give you a starting point:

You can factor an integer from each of those first to make it easier. For example:

36x^2 + 60x + 9 (I assume this is what you meant)
equals
3(12x^2 + 20x + 3)

If the equation is supposed to be equal to 0, you can just drop the 3 and get
12x^2 + 20x + 3

or you can leave it in place and just remember to keep it there throughout the rest of your calculation.


I will give you what I got as the answer, but I'd like to see your guess as to the correct answer before I do so, so I know that you at least attempted it.

Answer 2

1) 36 x^2 + 60 +9
= 3 (12x^2 +20x +3) = 3(2x+3)(6x+1)

2) 24x^2 - 46x + 10
= 2(12x^2 -23x +5)

Answer 3

1) Take out the common factor of 3 first: 3(12x^2 + 20 + 3). Start out by realizing that the numerical factors have to be 1 and 3 (to get the 3), and the signs in both factors have to be plus (to get both a positive middle term and a positive 3). Factor the bracketed part into (6x + 1)(2x + 3). Final answer is 3(6x+1)(2x+3).

2) Take out the common factor of 2 first: 2(12x^2 - 23x + 5). Start out by realizing that the numerical factors have to be 1 and 5 (to get the 5), and the signs in both factors have to be minus (to get a negative middle term and a positive 5) Factor the bracketed part into (4x - 1)(3x - 5). Final answer is 2(4x-1)(3x-5).

Answer 4

trinomials are expressions containing three terms.

The given expressions are quadratic trinomials.

1)
36x^2 + 60x + 9
= 3(12x^2 + 20 + 3)
=3(12x^2 + 18x + 2x + 3)
=3[6x(2x + 3) + 1(2x + 3)]
=3[(2x+ 3)(6x + 1)]

2)
24x^2 - 46x + 10
2(12x^2 - 23x + 5)
= 2(12x^2 - 20x - 3x + 5)
=2[(4x(3x - 5) -1(3x - 5)]
=2(3x - 5)(4x - 1)