Question

Factor: 6x^2 + 11x - 10
I know how to do the problem but i cant think of factors.

Answer 1

what multiplys to -10 but adds up to 11?

Answer 2

-60 and 11

Answer 3

multiplies*

Answer 4

thats not right...

Answer 5

Nope, you forgot that the coefficient of x^2 isn't 1. @hysusonic

Answer 6

we multiply 1 and c

Answer 7

*a

Answer 8

oh yea my bad @mathslover forgot about that

Answer 9

Either you divide by 6, and make the coefficient of x^2 as 1. And then move on.

But I usually prefer to follow quadratic formula and get the roots from there. And simply follow : \((x - \alpha) (x-\beta) \) .. .where \(\alpha\) and \(\beta\) are the roots.

Answer 10

\[6x^2+11x-10 \implies x^2+11x-60=0\]which two numbers multiply to give -60 and add 11?

Answer 11

actually, what factors of -60 add up to 11 ?

Answer 12

1 60
2 30
4 15 hmm, that looks good

Answer 13

-4 and 15

Answer 14

ah ok that helps :) thanks i can do the rest of the problems myself just needed the factors.....thanks all! :)

Answer 15

Oh okay :)

Answer 16

like here,

\(6 \left(x^2 + \frac{11}{6} x - \frac{10}{6} \right) \)

Find the roots of the equation in brackets. Roots are : 2/3 and -5/2

So, you can write it as : \(6 \left( x - \cfrac{2}{3}\right) \left(x + \cfrac{5}{2} \right) \)

Which further gives : \((6x - 4)(6x + 15) \)

So, roots are 4 and -15 !

Answer 17

those are almost factors, they are useful in finding the rest of it

Answer 18

mathslover explained it better than i would have lol

Answer 19

(x - 4/6) (x + 15/6) simplify

(x - 2/3) (x + 5/2) if theres still a bottom, put it back in front, thats where we got the 6 from

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

Answer 20

Yup!

Answer 21

I wonder the roots are 4 and -15 and not -4 and 15.

Or have I done something wrong?

Answer 22

15 and -4 are the roots... u have it right :P

Answer 23

\[\left(x-\frac{4}{6}\right)\left(x+\frac{15}{6}\right)=0\]reduce the fractions, and multiply diagonally whatever is unreducable. \[\left(x-\frac{2}{3}\right)\left(x+\frac{5}{2}\right)=0\]\[(3x-2)(2x+5)=0\]And then fromt here you just solve for x.

Answer 24

Oh, haha *highfive @amistre64 *

Answer 25

xD thanks guys! :D