week 6 math 10 how to properly format and solve a polynomial expression
For this weeks blog post I decided to make it on how to properly format a polynomial expression.
What is a polynomial expression? A polynomial expression is just an expression like any other, but it consists of mainly variables, exponents, constants and coefficients. One thing to note in finding and solving polynomial expressions is that we are not trying to find a definite answer, but we are mainly adding up our like terms.
our first example will be 6x²+2x+9-x+3x²
The first step in how to solve and properly format this polynomial equation is to add our common terms. In polynomials, we are only allowed to add similar terms together, so we are not allowed to add 6x² and 9 together because one has a variable and an exponent, and the other is a constant that doesn’t share anything with the other, so like I said we don’t do anything with the equation.
So adding together our terms will give us
9x²+9+x.
How did I get this answer? I’ll explain. I took the 6x² and added the 3x² to it, giving me 9x² because we only add the coefficients together. after that we took the 2x and the -x together. Since -x is equivalent to -1x, it gave us 1x but we can just remove the 1 away, because if there is only one x, it is known that there is an invisible 1 in front of it. After that, the 9 had no like terms so we just left it as it is.
Wait… there is still something wrong with the equation right now, and it has to do with the format of it.
9x²+9+x
This is formatted incorrectly for one reason. If we take a look at where each term is placed in the equation, one may say it is correct, which it technically is, the terms should be going from largest in value to least. So although the equation is correct, if we want to go a step further and properly format, we would put x in front of 9.
making our correct and properly formatted equation:
9x²+x+9.
The next example will be:
7x²+8x+3-2x²+x-2
Remember our first step is to add our like terms. So first it will be 5x² then 9x and then 1
So our final equation properly formatted will be:
5x²+9x+1
Why I chose this concept for my blog post is because I understood it well and I also believe that it is the most important basic information needed to succeed in polynomials.