show work please
2006-10-21 14:06:16 · 8 answers · asked by yankee_914 1 in Science & Mathematics ➔ Mathematics
6x² - 11x + 3 = (2x - 3)(3x - 1)
Working:
Product of 1st and last coefficient = +6 * +3 = +18
Now seek facors of + 18 that add to - 11 (the middle coefficient)
So they both have to be negative (to give a negative sum and a positive product)
18 = -1 * -18, -2 * -9, -3 * -6
The required pair are -2 and -9
Now use this fact to break up the middle term and then factorise as follows
So:
6x² - 11x + 3
= 6x² - 9x - 2x + 3
= 3x(2x - 3) - 1(2x - 3)
= (2x - 3)(3x - 1)
2006-10-21 14:09:06 · answer #1 · answered by Wal C 6 · 1⤊ 0⤋
Okay. 6x^2 means the first terms in your factors are each going to have an x and a number that multiplied with the other number will equal 6. Think 2 and 3. So now you have a 3x and a 2x.
Your middle term is a +3, with no x terms so it will probably by 3 and 1, either both positive or both negative. Now it's (2x ? 3) and (3x ? 3), or maybe the 3 and 1 are swapped.
You have to find a way to multiply the left term of one factor by the right term of the other factor, then add it to the product of the other terms to get -11x. 11? With 3s, a 2, an a 1 available, I'd guess 9 and 2. 3 * 3x = 9x; 2x * 1 = 2x; But remember, it's a negative 11x, so the right terms will both have to be negative. (Which works for the "+3" we worried about earlier.)
(2x-3)(3x-1)
2006-10-21 14:15:16 · answer #2 · answered by skepsis 7 · 0⤊ 0⤋
I'd start by rewriting this as 6x^2 - 11x + 3. The factors will be (ax + b) and (cx + d), where I don't know a, b, c, or d. But I do know that ac = 6 and bd = 3, and since the coefficient of x in the product is negative, I know that b and d are both negative. I only have a few options for a and c, and I suspect that they are 2 and 3 rather than 1 and 6. So looking at (3x - b)(2x - d), I need bd = 3 and 2b + 3d = 11. I see that 2*1 + 3*3 = 2 + 9 = 11, and 1*3 = 3, so my answer is (3x - 1)(2x - 3) = 6x^2 - 11x + 3.
2006-10-21 14:14:25 · answer #3 · answered by DavidK93 7 · 0⤊ 0⤋
6x^2+3-11x
first Arang them
6x^2-11x+3
Than 6*3=18(6 is 6x^2 and 3)
so M*N=18
M*N=11
so u got -9, -2
so u put 6x^2-9x-2x+3
then 3x(2x-3)+1(2x-3)
then the answer is (2x-3) (3x+1)
Good Luck with ur factor.
2006-10-21 14:25:13 · answer #4 · answered by INDI 2 · 0⤊ 0⤋
Solve the quadratic equation:
x^2 - (11/6)x + 3/6 =0 with the quadratic formula. find the two roots, say x1, x2.
The factorization will be:
(x - x1)(x - x2)
2006-10-21 14:26:44 · answer #5 · answered by Dr. J. 6 · 0⤊ 0⤋
Make sure you thank everyone for doing your homework for you.
2006-10-21 14:13:22 · answer #6 · answered by northyankeefun 3 · 0⤊ 0⤋
2x-3)(3x-1)
2006-10-21 14:11:53 · answer #7 · answered by 7 · 0⤊ 0⤋
(3x-1)(2x-3)
2006-10-21 14:14:09 · answer #8 · answered by pilly 2 · 0⤊ 0⤋