havent a clue!

6x2+x-15=0

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- Dec 21st 2007, 11:26 AMjenkohavent a clue!
havent a clue!

6x2+x-15=0 - Dec 21st 2007, 11:37 AMtopsquark
Let's try this using the method I posted in your other thread.

Mulitply 6 and -15: -90

Now list all pairs of factors of -90:

1, -90

2, -45

3, -30

6, -15

9, -10

10, -9

15, -6

30, -3

45, -2

90, -1

Now which of these pairs add to 1? The 10 and -9, of course. So 1 = 10 - 9:

$\displaystyle 6x^2 + x - 15 = 0$

$\displaystyle 6x^2 + (10 - 9)x - 15 = 0$

$\displaystyle 6x^2 + 10x - 9x - 15 = 0$

$\displaystyle (6x^2 + 10x) + (-9x - 15) = 0$

$\displaystyle 2x(3x + 5) - 3(3x + 5) = 0$

$\displaystyle (2x - 3)(3x + 5) = 0$

So set each factor equal to 0:

$\displaystyle 2x - 3 = 0 \implies x = \frac{3}{2}$

or

$\displaystyle 3x + 5 = 0 \implies x = -\frac{5}{3}$

-Dan - Dec 21st 2007, 11:42 AMcolby2152
BTW, after a lot of practice of factorials, you will be able to look at them for a couple seconds and know what the constants will be.

I understand your plight. When I was a kid learning about factoring, my teacher didn't even show me about the additives and multiples that make up the constants right away. Needless to say, I taught it to myself.(Tmi) - Dec 21st 2007, 11:52 AMjenko
i know the basics of mathematics e.g multiples etc it jus some of the terminologies that are used which i have never heared of or are unsure of ite been a while since i have done this last time i done then wen i was in high school two years ago and ever since that day i forgot it all as i thought i would never use it on it later life which i realy regret otherwise i wouldnt be here now or better still would be here with even more harder questions for you guys to help me with! :D