factoring algebriac expressions

[Gurpinder]

hello math friends,

i am having hard time understanding how to factor trinomials. i dont get it.

can someone please factor this 12a^2 + 5ab− 3b^2 and explain me the process of how to do it.

thanks all

[4GMAT_Mumbai]

Hi Gurpinder,

Step 1: Multiply the coefficients of a^2 and b^2. In this case (12 times -3 = -36)

Step 2: What would be two numbers such that it would yield the product (figured out in step 1) and such that it would add up to yield the coefficient of ab (+5 in this case)

The numbers would be 9 and -4 in this case. 9 times -4 = -36 and 9 + (-4) = 5

Step 3: Split the equation in terms of the numbers figured in step 2

so, the equation becomes 12 a^2 - 4ab + 9 ab - 3b^2

Take out the common items from the first two items. Do the same for the last two items.

it becomes 4a * (3a - b) + 3 * (3a - b). It has thus crystallized into sum of two terms.

Take out the common items from these two terms.

(3a - b) * (4a + 3) is the net equation.

Hope this helps. Please pm me in case you need further clarifications.

Thanks.

[mj78ind]

Divide through out by b^2 and substitute a/b = x then we have,

12x^2 +5x - 3 =0

Now this is a quadratic in x and it can be solved......

[outreach]

12a^2 + 5ab- 3b^2

roots should have sum of '5'
roots should have product of '-36'(12*-3)

only 9,-4 can be the roots

so eq is
12a^2 + 5ab- 3b^2
12a^2 + 9ab-4ab- 3b^2
3a(4a+3b)-b(4a+3b)
(3a-b)(4a+3b)