Degree of Polynomials Degree of Polynomials Polynomial can be defined as an expression that consists of constants values, variables and exponent values and combined with mathematical operator are said to be polynomials. Note: - The polynomial expressions are not combined with the division operator. In polynomial expression the exponent can be anything 0, 1, 2, 3, 4, 5, and 6 ….etc. In mathematics, the polynomial expression cannot have infinite values. For example: 2xy2 – 3x + 5y3 – 36. This given expression a is polynomial expression, in this expression the exponent value is 0, 1, 2 and 3. The exponent values of polynomial expression are also said to be the degree of polynomial. So in the above expression the degree of polynomial is 0, 1, 2 and 3. And also negative and fractions values are not involved in the polynomials expressions. For example: 4xy-4 and 2/y + 3. Given expression are not polynomial because it contain negative exponent values and fractions values. In mathematics, the polynomial expression are sometimes also named for their degrees.Let we have second – degree polynomial expression, that is 4p2, p2 – 10, or ax2 + bx + c, it is sometimes also known as 'quadratic equation'. Now we have third – degree polynomial expression, that is - 3p3, p3 – 36, it is sometimes also known as 'cubic equation'. Suppose we have forth – degree polynomial, that is 4p4, 3p5 + 15, it is also known as 'quartic equation'. In case of fifth – degree polynomial, that is 6p5, p5 – 5p3 + p - 10, it is sometimes also known as 'quintic equation'. Know More About :- How to do Short Division
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Let's discuss how to solve the polynomial expression. We can also solve the the polynomial expression using calculators, the calculators are as follows: Polynomial calculator, rational expression, Radical expressions, solving equations, these following calculators are used to calculate the polynomial equations. These equations are in the form of x (a) = y (b), here these values x (a) and x (b) are polynomials. Now we will discuss some of the specials cases for such equations are Linear equation that is in the form of (5x + 5 = 6). Quadratic equations that is in the form of (4x2 + 6x – 10 = 0) .And cubical equation which is in the form of (8x3 + 5x2 – 6x + 8= 0); Let's discuss how to solve polynomial expression. Example: Suppose we have a polynomial equation: 4x2 – 2 + 3x + 2 = x2 – 4 + 1 2 4 5 4 Then solve this polynomial expression: Solution: Here we need to follow some steps to solve this expression: Step1: Eliminate factors of this equation by multiplying each side by the least common denominator. In this polynomial equation the value of least common denominator is 20, so multiply 20 on both sides of the equations. On multiplying 20 on both sides we get: 4x2 – 2 + 3x + 2 = x2 – 4 + 1 2
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20 * 4x2 – 2 + 20 * 3x + 2 = 20 * x2 – 4 + 20 * 1 2 4 5 4 10 (4x2 – 2) + 5 (3x + 2) = 4 (x2 – 4) + 5; Step2: Now solve each side by avoiding the parenthesis and then combine the like term present in the expression; 10 (4x2 – 2) + 5 (3x + 2) = 4 (x2 – 4) + 5; 40x2 – 20 + 15x + 10 = 4x2 – 16 + 20; Read More About :- Algebra Polynomials
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