Factorise the following:

6x^2-11x-10

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- Oct 17th 2009, 10:26 PMTessarinaFactorising a quadratic trinomial
Factorise the following:

6x^2-11x-10 - Oct 17th 2009, 10:54 PMalexmahone
- Oct 17th 2009, 10:56 PMGrandad
- Oct 18th 2009, 04:37 AMaidan
Hi Tessarina,

this might assist:

The factors of 6 (call them a & c)

1 x 6 = 6

2 x 3 = 6

The factors of 10 (call them b & d)

1 x 10 = 10

2 x 5 = 10

Since -10 is negative you know that one of the signs will be.

You are looking for this form:

(ax - b)(cx + d) or (ax - d)(cx + b)

We already know the factors (coefficients) that will give: 6x^2 & -10

We are seeking the middle part

such that

ax*d - cx*b = -11x

or

ax*b - cx*d = -11x

We are trying to find -11x in the following:

--------------------------------------

plugging in the factors (1,6 & 1,10)

(**1**x -**1**)(**6**x +**10**)

**1**x***10**-**6**x***1**= 4x (does not equal -11x)

or

(**1**x -**10**)(**6**x +**1**)

**1**x***1**-**6**x***10**= -59 (does not equal -11x)

plugging in the factors (1,6 & 2,5)

(1x - 2)(6x + 5)

1x*5 - 6x*2 = -1x (does not equal -11x)

or

(1x - 5)(6x + 2)

1x*2 - 6x*5 = -28x (does not equal -11x)

plugging in the factors (2,3 & 1,10)

(2x - 1)(3x + 10)

2x*10 - 3x*1 = 17x (does not equal -11x)

or

(2x - 10)(3x + 1)

2x*1 - 3x*10 = -28 (does not equal -11x)

plugging in the factors (2,3 & 2,5)

(2x - 2)(3x + 5)

2x*5 - 3x*2 = 4x (does not equal -11x)

or

(2x - 5)(3x + 2)

2x*2 - 3x*5 = -11x (what is needed ! )

The result wanted:

(2x - 5)(3x + 2) = 6x^2 -11x - 10

::

After you do this a few times alexmahone's method will be easy to use and generate the result;

after a few more times you will be able to do it immediately the way Grandad can.

The asterisk (*) used above denotes multiplication.

. - Oct 18th 2009, 05:29 AMmr fantastic
Of related interest: http://www.mathhelpforum.com/math-he...tml#post385857