This week in Math 10 we learned how to factor hard/ugly polynomials. A lot of factoring hard/ugly polynomials had to do with “trial and error”, which means to plug in numbers and test them to see if they work, but in a logical and thinking way. Using the “trial and error” method is good but after a while it gets harder when the coefficients start getting larger and there are more variable, that is when we learned the box method which is like factoring magic.
Here is a diagram I made of which types of polynomials you use this method for, how you execute this method and how to check if you executed it right:
The type of polynomial I used as an example is a hard/ugly trinomial because it cannot be factored by using the x^2 method or the difference/perfect square method.
How would you execute this? first you want to draw a box with 4 sections and place the first term in the top left section and place the last term in the bottom right corner, by now you should only have 2 sections open, in order to find what numbers and variables to put into those sections you need to multiple the first coefficient and last coefficient. Once you get an answer you need to find 2 numbers that add to the middle term but multiply to the answer you just got, once you have your 2 integers place them with the variable to fill up the last 2 empty sections. Now you have to do the final step which is factor the terms in the box up and down and left and right. Once you do that step make your 2 brackets and place your answers in.
You might be asking how do I know the answer is right. All you have to do is reverse your steps and use the FOIL/Claw method and you should get the original equation.
Terms/Definitions:
factor hard/ugly polynomials- is when you cannot use any other methods to solve the polynomial.
trial and error- to try different numbers logically and plug them in and check if it works.
coefficients- the numbers beside the variables.
variable- the letters/unknown numbers beside the coefficient.
box method- to factor with a GCF box.
FOIL/Claw method- first, outside, inside, last.