Factoring

Twolvesfan14 · #1 $Old$ 01-02-2008, 02:26 PM

Hello everyone,

I am completely blank on factoring imperfect questions such as this:

12m^2 + 7m - 10

I understand that the normal application to do a question such as this is to find 2 factors that, when multiplied, are -10, and, when added, are 7. Since there are no two whole numbers that multiply to -10 and add to 7, I am at a complete loss.

Thank you all very much
Twolvesfan14

colby2152 · #2 $Old$ 01-02-2008, 02:40 PM

Quote:

Originally Posted by Twolvesfan14 $View Post$

Hello everyone,

I am completely blank on factoring imperfect questions such as this:

12m^2 + 7m - 10

I understand that the normal application to do a question such as this is to find 2 factors that, when multiplied, are -10, and, when added, are 7. Since there are no two whole numbers that multiply to -10 and add to 7, I am at a complete loss.

Thank you all very much
Twolvesfan14

Use the quadratic formula:

$m = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

where a = 12, b = 7, and c = -10

galactus · #3 $Old$ 01-02-2008, 02:46 PM

This factors rather nicely.

$12m^{2}+7m-10=0$

What two numbers when multiplied equal -120(not -10, that's your mistake) and when added equal 7?.

Uhhhh, let's see, 15 and -8. (15)(-8)=-120 and 15-8=7.

$12m^{2}+15m-8m-10$

Group and factor:

$(12m^{2}+15m)-(8m+10)$

$3m(4m+5)-2(4m+5)$

$\boxed{(3m-2)(4m+5)}$

bobak · #4 $Old$ 01-02-2008, 02:50 PM

Quote:

Originally Posted by Twolvesfan14 $View Post$

$12m^2 + 7m - 10$

use latex it is easier on the eye

Quote:

Originally Posted by Twolvesfan14 $View Post$

I understand that the normal application to do a question such as this is to find 2 factors that, when multiplied, are -10, and, when added, are 7. Since there are no two whole numbers that multiply to -10 and add to 7.
Twolvesfan14

that is only correct if the term with x^2 has a coefficient of 1, which is not the case here is it?

You must consider how 12 may factor and also how you may factor 10

$12 = 2^2 \cdot 3$
$10 = 2 \cdot 5$

now you start filling out the factors.

$(12m+ ? ) \cdot (m + ?)$

now you try the possiblites like this, you may see that it is unsucessful

then you may want to give this a go
$(4m+ ? ) \cdot (3m + ?)$

you may find this to be more sucessful.