In Mathematics, a polynomial is an expression that consists of variables, constant, and mathematical operators. The exponents of the variables are positive integers, whereas the constants are real numbers. The polynomial cannot have a negative value exponent, variable in the denominator, variable inside the radical sign. The three primary terminologies used in the polynomials are coefficients, degrees, and the variable. The important process in polynomials is factorization. While factoring polynomials, we can get the zeros of the polynomials. Let us discuss these terms with the help of an example.
Consider an example, 4x2 + 10y – 3
The variables in the above-given examples are x and y. The coefficients are the constant values present before the variables. Here, the coefficients are 4, 10, -3. The highest power of the variable in the expression is called the degree. In this case, the degree of the given polynomial is 2. Now, let us have a look at the basic operations of polynomials. The basic operations are:
- Addition of Polynomials
- Subtraction of Polynomials
- Multiplication of Polynomials
- Division of Polynomials
Addition and Subtraction of Polynomials
In addition and the subtraction of polynomials, first, arrange the like terms, and the like terms are added together.
For example, 4x +10y and 6x + 4y are the two polynomials. Now, we have to add polynomials.
Now, arrange the like terms together , (4x +10y) + ( 6x + 4y )
Here 4x and 6x are the like terms, 10y and 4y are the like terms
= 4x + 6x + 10y+ 4y
Now, add the like terms, we get
10x + 14y, which is the result of the given polynomial
In the process of polynomial multiplication, multiply each term in one polynomial by each term in the other polynomial. Now, add those answers, and simplify the answer, if it is needed.
Let us take an example (4x+ 2y+1)(2x + 2) are the two polynomials. Follow the steps mentioned above, to get the product.
(4x+ 2y+1)(2x + 2) =8x2 + 8x + 4xy + 4y + 2x +2
Now, perform addition operation, we get
8x2 + 4xy +10x + 4y+ 2.
The polynomial long division method is used for dividing polynomials, which is the generalized version of the arithmetic method called the long division method. In this method, the division of one polynomial by another polynomial is performed, which should have the same or the lower degree.
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