Question 212909: HOW TO FACTORISE THIS QUESTION WITHOUT USING THE QUADRATIC FORMULA METHOD BUT EITHER CROSS OR GROUPING METHOD
12X^2-45X-12=0
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! First factor the common factor of 3.
12x^2 - 45x-12=0
3(4x^2 -15x-4)=0
Next you have what I call "Advanced Trinomial Factoring", which I like a trial and error method. The middle term being an ODD number, means that you must NOT use an even times even combination (like 2x*2x won't work for the FIRST times FIRST!) It MUST be 4x*x!
3(4x____)(x_____) = 0
The last times last also cannot be 2*2, but must instead by 4*1 or 1*4. What works here is to place the 1 on the first blank line and 4 on the second blank line.
3(4x___1)(x__4) = 0
Now, the signs must be OPPOSITE sign, so as to get the last term to come out negative. In this case, make the 4 a -4 and the 1 a +1. This gives you a middle term of -15x.
3(4x+1)(x-4) = 0
Set each factor equal to 0. The 3 has no effect on the solution!
4x+1= 0
4x=-1
x=-1/4
x-4=0
x=4
If you need an informal explanation of this type of factoring, together with examples, exercises and answers, please see my own website. Do a "Bing" search for my last name "Rapalje" and look for "Rapalje Homepage" near the top of the search list. Click on the link "Basic, Intermediate and College Algebra: One Step at a Time" near the top of my Homepage. Select "Basic Algebra", and look in "Chapter 2" for the topic "Advanced Trinomial Factoring". See also my "MATH IN LIVING COLOR" pages where you will find a lot of these problems solved, IN COLOR of course!
R^2
Dr. Robert J. Rapalje, Retired
Seminole Community College
Altamonte Springs Campus
Florida
|
|
|
