Week 5 – On solving polynomial expressions

This week, we started on solving polynomial expressions. One thing I was noticed was that most of these expressions appear in the form of:

, and a number

And I would like to share a really interesting method for solving these equations, introducing the cross factoring method, which involves a LOT of guessing and elimination.

For example, take this one, in this question I need to find out if X+5 is one of the factors constructing the expression below:

First I need to find the “number combinations” for the first and last numbers, in which I came up with a conclusion:

Then, I first multiplied the top left “half” to the bottom right “half”,(in this case, is 3X and 5) and so on doing the other pair diagonally.

Next, I get the equation of , which makes up the middle 13X in the original equation.

Finally, to get the simplified equation, I get to “combine” them horizontally and get , it has a factor of x+5

Now you might ask something like, “why can’t it be 1 and -10?” Put simply, these number to be multiplied diagonally and the sum of those number must be equal to the middle product of the “two ends”, if this is wrong, then the user of this method must use another pair until it makes sense, sometimes changing both sides. (by the way, if the aforementioned pair continues to go on then we will get )