2006-07-17 06:15:20 · 11 answers · asked by cityturtleblue 2 in Science & Mathematics ➔ Mathematics
I think it is (Listen in Class * Study ) = answer.
2006-07-17 06:20:26 · answer #1 · answered by Todd V 3 · 0⤊ 0⤋
1. Take out a factor. 2 goes into all coefficients, so multiply the entire equation by 2, and you'll get...
2(12x^2 - 5x - 2)
2. Now factor the quadratic equation using conventional methods while ignoring the 2 at the beginning. You will put the 2 at the beginning of the factored equation, but that's later.
(a)(c) = (12)(-2) = -24
We have to split the equation apart and to do that, we must split the middle coefficient. (a)(c) does this, and it is -24.
Now find all the possible problems that come out -24.
(-8)(3) is one of them. Also, (-8 + 3) = -5, which is the middle coefficient. So now we know how we are going to split. You should have...
(12x^2 - 8x) + (3x - 2) = 0
3. Now that you have split it into (12x^2 - 8x) + (3x - 2) = 0, simplify it.
(3x - 2) ---> Already simplified, there's nothing else to do.
(12x^2 - 8x) :: There are multiple ways to simplify this, but you want to come out with all whole numbers, and no fractions. The best way to do that is to simplify it to...
4x(3x - 2) :: the factor is also the same as the second factor already simplified... so you have...
4x(3x - 2) + (3x - 2) = 0
Simplify it further... Since you have two of the same factors, you can multiply the coefficients by the factor. The coefficients that we have left are 4x and 1. Soooo...
(4x + 1)(3x - 2) = 0
Remember the 2 from the very beginning, sooo...
2(4x + 1)(3x - 2) = 0
2006-07-17 15:29:22 · answer #2 · answered by trancevanbuuren 3 · 0⤊ 0⤋
A simple first step is to factor out the number 2.
2(12x^2 - 5x - 2)
The trinomial factors, if it can be factored, will be of the form
(ax + b)(cx + d)
The factors of the coefficient of x^2 are 1, 12, 2, 6, 3, 4 and the factors of the constant term are 1, 2.
Using this information you might, by trial and error, find values of a, b, c & d that do the job.
The factored result here is 2(4x + 1)(3x - 2)
For an easy way fo factor the above, see the Purplemath lesson linked below.
2006-07-17 13:34:16 · answer #3 · answered by kindricko 7 · 0⤊ 0⤋
24x^2-10x-4
sum of factors is -10
product of factors is 24*-4= -96
so by trying the factors of 96; we come to the conclusion that the numbers are -16 and 6
24x^2-10x-4 = 24x^2 -16x +6x-4
= 4x(6x-4) +1(6x-4)
= (4x+1)(6x-4)
4x+1=0 or 6x-4=0
therefore x= -1/4 or x=2/3
2006-07-17 13:32:45 · answer #4 · answered by Syed Baqir Rizvi 2 · 0⤊ 0⤋
24x^2-10x-4
= (6x - 4)(4x + 1)
2006-07-17 13:21:13 · answer #5 · answered by Kish 3 · 0⤊ 0⤋
24x^2 - 10x - 4
2(12x^2 - 5x - 2)
2(3x - 2)(4x + 1)
2006-07-17 16:30:02 · answer #6 · answered by Sherman81 6 · 0⤊ 0⤋
24x^2-10x-4=(8x+2) (3x-2)=2(4x+1)(3x-2)
2006-07-17 13:21:37 · answer #7 · answered by raj 7 · 0⤊ 0⤋
2(12x^2 - 2x - 4)
2(4x + 2)(3x - 2)
2006-07-17 15:55:10 · answer #8 · answered by jimbob 6 · 0⤊ 0⤋
24x^2-10x-4
=2(12x^2-5x-2)
=2(12x^2-8x+3x-2)
=2(3x-2)(4x+1)
2006-07-17 13:21:30 · answer #9 · answered by amit 1 · 0⤊ 0⤋
2(4x+1)(3x-2)
2006-07-17 18:54:12 · answer #10 · answered by creative_idea_thinker 2 · 0⤊ 0⤋