Dividing Polynomials Dividing Polynomials In order to learn about Dividing Polynomials, first we must know that the polynomial by which we divide the given polynomial is called the divisor and the polynomial which we are dividing is called the dividend. Now if the divisor is a monomial, then we will divide each term of the dividend with the divisor and we get the quotient. We will split the polynomial to be divided from + or - sign in the dividend and write the divisor under each of the terms. Let us see it in this example: Divide the polynomial 5x^4 + 20x^3 + 15x by 5x, we can write the above expression as follows : = 5x^4/5x + 20x^3/5x + 15x/5x Now looking at the each expression individually, we divide the coefficients of the terms separately and the variables are divided separately, so that the powers of the denominator are subtracted from the power of the numerator and we get: X^3 + 4*x^2 + 3 as the quotient of the above polynomial division.
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Some times when we proceed to divide the polynomial with another, then rearrangement of the numerator or the denominator will help us to get the solution to the given division problem. So we look at the following example for the same: 2x^2 + 2x divided by ( x + 1 ) This division cannot be performed by the method given above, so we proceed in the following way : We first take 2x as a common factor of the dividend and so it will be written as follows: = ( 2x^2 + 2x ) / ( x + 1 ) = 2x * ( x + 1 ) / ( x + 1 ) Cancelling ( x + 1 ) from the numerator and the denominator, we get : = 2x Ans. Now we look at the problem where the divisor is not a monomial, it may be a binomial or trinomial. In such cases, we ensure that the divisor and the dividend are arranged in the descending order of the power of their variables, if they are not so. Now we will take the first term of the divisor and check the multiple of it for the first term of the dividend and then we divide. This method is called the long division method. Let us take and example : divide ( x^2 + 2x + 7 ) by ( x – 2 ) To solve the problem of division, we say that the following steps are to be followed : 1. First we will divide the first term of the numerator by the first term written as the divisor and we put it as the answer.
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2. Now we will multiply the denominator by that answer and write it below the numerator 3. Now we find the difference and form a new polynomial for which same process is repeated until we get the degree of the remainder smaller than the divisor. In this way we can divide one polynomial from another We can use online tutor to study about left and right hand limits and its related problems. We have online Andhra Pradesh Board Computer Science books, from which a child can prepare different topics of the subject and appear for the specific examination for any grade.
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