factoring for two binomials with like terms?

Question

1. 3x^2 + 5x + 2=
2. 5x^2 + 11x + 2=
3. 3x^2 - 8x + 4=

Please solve and explain how to do.

Answer 1

Hi! I will do my best to show you how I arrived at my answers, However, it is rather difficult to help with math homework without being able to physically illustrate the steps to someone.
Before I work out the steps, I will show you my logic in solving these problems. Since each problem has their leading coefficient (the first actual real number prior to the x^2) as a non-factorable prime number, you can always break your binomial into two factors as such (3x or 5x +/- .....) (x +/- .....) for the .... portion, you will have to depend upon the interaction of the second and third terms, in accompaniment with the leading, to decide what it/they will be. You can do this breakdown with leaving the prime number with one x and leaving the other x and 1x everytime you have a binomial with a leading prime coefficient. Okay, that made no sense, I'm super sorry, I just do not know how else to explain it. Huh, well, let me show you my steps and then maybe it will make more sense to you:
1). 3x^2 +5x +2 =
(3x + 2) (x +1) you can check this by undoing what we did to see if it equals the original equation.

2). 5x^2 + 11x + 2 =
(5x+1) (x+2)

3). 3x^2 - 8x + 4=
(3x-2)(x-2)


I hope that this helped. Maybe you should consider asking your teacher/parents/peers for further assistance. Good luck! : )

Answer 2

there's a kind of short cut way to do these types of problems . .

3x^2 - 8x + 4 . . . . multiply the coefficient of the 1st term and the last term . . . 3x4=12 . . . now use this number and find all the factors that multiply to get 12 but add or subtract to get the middle terms coefficient (8) . . . . you have 1x12 and 2x6 and 3x4 . . . 2+6=8, so pick 2 and 6 . . . now we will substitute these back into the original problem . . .


3x^2 - 8x + 4
3x^2 - 2x - 6x + 4 . . . then make 2 groups
(3x^2 - 2x) - (6x - 4) . . now find the GCF
x(3x - 2) - 2(3x - 2) . . notice you have the same thing in each set of parentheses . . now you can factor again . .
(x - 2) (3x - 2) . . this is your answer!!

I know it's probably kind of hard to understand it this way . . but email me at [e-mail] and maybe I can scan a handwritten example and email it to you . . .

Answer 3

1 ( 3x+ 2 ) ( x +1 )

2 ( 5x + 1 ) ( x + 2 )

3 ( 3x - 2 ) ( x + 2 )

Answer 4

i use magic...
hard to explain...go to ur teacher for help
but,,,(3x+2)(x+1)
(5x+1)(x+2)
and
(3x-2)(x-2)
ten points for first to answer!