Factor by grouping

Question

30x² + 12x-25x - 10

 

How do i do this step by step?

Answer 1

30x² - 13x - 10 = (5x + 2)(6x - 5) by the method of trial and error allocation of various factors of 30 and 10 so that when FOIL is done, the "middle terms" combine to give net -13x.

 

Pay lots of attention to the lectures (and texbook examples) in Algebra class.

 

Jump into testing various possibilities, when asked to factor. As Edison said about failure, it teaches you which trials do not work! This is a skill that you MUST learn. Take advantage of after school free tutoring, of a good peer group, and take a look at Khan Academy or other similar things onYoutube.

 

 

Answer 2

We being by collecting like terms, so that the equation now reads:

 

30x² - 13x - 10 = 0

 

Remember that in this statement, that the 2nd sign tells you that the signs in the parentheses are unalike; while the other sign tells you that the largest absolute value number is a negative number.

 

Next, best to start off with the two parentheses with:  (6x    )  and (5x     )

 

Then, we want to figure out which 2 numbers multiplied together give one a negative 10, but combined together, gives a net result of (-13x); which means we think through the following:

 

First, most likely numbers for getting the constant of 10 are:  5 and 2 or 2 and 5

 

So, let's try:

 

(6x  -   5) (5x  +   2)

 

Which puts us at:  30x² + 12x - 25x - 10

Which is:  30x² - 13x - 10

 

 

Answer 3

Factor the first two terms and last two terms separately.

 

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

 

 

The common factor is (5x + 2).

 

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