Degree of a Polynomial Degree of a Polynomial The degree of polynomial is the greatest exponent of a term. The greatest exponent should have a non-zero coefficient in a polynomial expressed as a sum or difference of terms which is commonly known as Canonical form. The sum of the powers of all variables in the term is the degree of the polynomial. The degree can also be specified as order. The degree of polynomial is for the single variable or the combination of two or more variables with the powers. Properties of Degree of Polynomial According to the degree of polynomials the names are assigned. Below listed are the degree of polynomials: --- The name of the zero degree polynomial is constant. --- The name of the 1 degree polynomial is linear. --- The name of the 2 degree polynomial is quadratic. --- The name of the 3 degree polynomial is cubic. --- The name of the 4 degree polynomial is quartic Know More About What is the Dependent Variable

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--- The name of the 5 degree polynomial is quintic. --- The multiplicative inverse 1a have degree -1 --- The square root has a degree as 12 --- The logarithm has a degree as 0, example log b. --- The exponential functionâ€™s degree is infinity. How to Find the Degree of Polynomial In this section, learn how to find the degree of polynomial Using one variable : Let us consider the polynomial, 8x3 + 7x4 + 6x2 + 5x + 1. The degree of the first term is 3. The degree of the second term is 4 The degree of the third term is 2 The degree of the fourth term is 1 and The degree of the last term is 0. Here the greatest degree among all the degrees is 4. So the degree of the polynomial 8x3+7x4+6x2+5x+1 is 4. Using two variables : Let us consider the given polynomial is 5x2y4+2xy3+8y2+2y+x3+1 The degree of the first term is sum of the power of x and y. So the degree for the first term is 2+4 which is 6. The degree of the second term is 1+ 3=4. The degree of the third term is 2. The degree of the fourth term is 1. The degree of the fifth term is 3 and The degree of the last term is 0. Here the maximum degree is 4. So 4 is the degree of the polynomial 5x2y4+2xy3+8y2+2y+x3+1 Learn More Adding Polynomials Math.Tutorvista.com

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Division of Polynomials Division of Polynomials In this article we are going to discuss about dividing polynomials. In arithmetic, long division is the standard procedure that is suitable for dividing simple or complex multi digit numbers. It breaks down a division problem into a series of easier steps. As in all division problems a one number is called the dividend, the divided by another, called the divisor, producing a result called the quotient. Polynomial Division Below are the problems based on polynomial division Example 1 : Divide the given polynomial equation (14x3 + 24x + 19) by (x + 2) using long division method. Solution : Given polynomial equation is (14x3 + 24x + 19) Dividend is (14x3 + 24x + 19) and divisor is (x + 2) ________________ (x + 2) ) 14x3 + 24x + 19 ( (14x2 - 28x + 80) 14x3 + 28x2 ( - ) Math.Tutorvista.com

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______________ - 28x2 + 24x + 19 - 28x2 - 56x ( - ) ________________ 80x + 19 80x + 160 ( - ) _______________ - 141 ______________ Quotient = 14x2 - 28x + 80 and remainder value is - 141 Answer : The final answer is Quotient = 14x2 - 28x + 80 and remainder value is - 141 Example 2 : Divide the given polynomial equation (6x3 - 10x2 + x) by (x - 2) using long division method. Solution : Given polynomial equation is (6x3 - 10x2 + x) Dividend is (6x3 - 10x2 + x) and divisor is (x - 2) Quotient = 6x2 + 2x + 5 and remainder value is - 10 Answer : The final answer is Quotient = 6x2 + 2x + 5 and remainder value is - 10 Example 3 : Divide the given polynomial equation (3x4 + 12x3 + 7x2 - 1) by (x + 3) using long division method. Solution : Given polynomial equation is (3x4 + 12x3 + 7x2 - 1) Dividend is (3x4 + 12x3 + 7x2 - 1) and divisor is (x + 3) Read More About Polynomial Equation

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Degree of a Polynomial

Published on Apr 14, 2012

The degree of polynomial is the greatest exponent of a term. The greatest exponent should have a non-zero coefficient in a polynomial expres...

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