Dividing polynomials is not an easy task as it seems. Sometimes the polynomials equations include higher degree that is why it is difficult to solve it. Basically, the polynomial equation is same as the algebraic or the quadratic equation. But the major difference between both is the algebraic equation does not contain degree on variables, but quadratic includes it. The polynomial equation usually contains same variables in the quadratic form. To better understand consider an example which is suitable-
3a + 2b = 18 algebraic equation
x²+2x+ 8=0 Polynomial equation
When you are dividing polynomials, and then feel some difficulties. Due to lack of knowledge of mathematics operation and the complexity of polynomial; makes it more difficult. The variables include different values that are why it is hard to solve. There is no direct method to solve polynomial equations.
When you are looking for understating the dividing the polynomial consider an example.
This is divided by
The dividing rule is same as we have performed in previous classes. But the variable in dividing polynomials makes complexity in solution.
Take the figure in this form as below
To solve this polynomial determine the degree of both the equation. As shown in the first equation has 3 higher degrees and the second includes one.
In the first step of division, to need to divide first equation by x²
We take x² because it can eliminate the (x³) from the equation. In a first step, we can eliminate the higher degree than we go to the lower degree.
After division we have,
Now you have to follow the second step in which, the elimination of second-degree performs. Divide the equation with ‘5x’ that can help you to eliminate the term 5x².
Now we have taken 5 with the variable it is done to eliminate both x² and 5 from the equation. After dividing the above equation, you will get,
Now we have eliminated the first and second degree. Now you have to eliminate the variable which includes a single degree. For this purpose, we need to repeat the previous step with different numerical values. Divide the above equation by (x-2) with (-3)’s multiplication. This will help you to eliminate (-3x) from the equation.
After division, you have 0 remnants. So, keep the numbers which are multiplied by the divider. Above we used
x² , 5x and -3
We need to add these results to get the final answer.
Hence the solution of this equation is
Basically, it is not difficult to solve the equation, but it needs huge grip in a calculation, division, multiplication and much more. Also, it needs great basic knowledge of mathematics for dividing polynomial. In the current, the polynomial equation is taken to know the intelligence of people. That is why it is used in many competitive exams. It makes the brain exercise perfect and helps to master in a calculation. It is beneficial for us so, we need to practice more and more to understand the division polynomial. After regular practice, you can become a master in it.