Algebraic Equation Solver Algebraic Equation Solver Algebra equations are the equations of the form algebraic variables with some numerical coefficient. Algebra equation contains the terms like numbers, integers, fractions, roots, exponents, ratios, graphing etc. Pre algebra equation is the simple equation which can be solved easily without any complex calculations. Linear equation is an algebraic equation in which each term is either a constant or the product of a constant and with a single variable. It contains one or more variables. It occurs with great regularity in applied mathematics. Algebra Equation Solver Algebra equation solver is to solve the equation and to get the value of variables. The following are the important things that need to be noted down in algebra equations Variables : The variable is the important thing that needs to be considered in equations. Operations : Operations such as (+, -, x, /) are the operations that plays an important role solving equations. Know More About Addition Property of Equality
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Values : We should enter the correct and valid values to get a perfect answer in solving equations. Solve x + 3 = 0 To get the value x send +3 to other side, we get x = -3. Therefore, x is -3. It is very simple. It only deals with whole numbers in the above example. Solving Algebraic Equations Below are the examples on solving algebraic equations: Example 1 : Solve 2x + 12 = 0 Put all the variables on one side and values on other side. We get, 2x = -12 Now to get x value divide both sides with 2 2x2 = −122, x = -6 2) Solve the equation x2 - 4 = 0 X2 - 4 = 0,
Add 4 on both the sides we get,x2 = 4
To avoid a square put square root on both the sides X = √4 , x = 2 Learn More What is Dependent Variable Math.Tutorvista.com
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How to Factor a Polynomial How to Factor a Polynomial Factoring Polynomials refers to factoring a polynomial into irreducible polynomials over a given field. It gives out the factors that together form a polynomial function. A polynomial function is of the form xn + xn -1 + xn - 2 + . . . . + k = 0, where k is a constant and n is a power. Polynomials are expressions that are formed by adding or subtracting several variables called monomials. Monomials are variables that are formed with a constant and a variable of some degree. Examples of monomials are 5x3, 6a2. Monomials having different exponents such as 5x3 and 3x4 cannot be added or subtracted but can be multiplied or divided by them. Any polynomial of the form F(a) can also be written as F(a) = Q(a) x D (a) + R (a) using Dividend = Quotient x Divisor + Remainder. If the polynomial F(a) is divisible by Q(a), then the remainder is zero. Thus, F(a) = Q(a) x D(a). That is, the polynomial F(a) is a product of two other polynomials Q(a) and D(a). For example, 2t + 6t2 = 2t x (1 + 3t). Variables, Exponents, Parenthesis and Operations (+, -, x, /) play an important role in factoring a polynomial.
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Factorization by dividing the expression by the GCD of the terms of the given expression: GCD of a polynomial is the largest monomial, which is a factor of each term of the polynomial. It involves finding the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) of the terms of the expression and then dividing each term by its GCD. Therefore the factors of the given expression are the GCD and the quotient thus obtained. Example 1 : Factorize : 2x3 – 6x2 + 4x. Solution : Factors of 2x3 are 1, 2, x, x2, x3,2x, 2x2, 2x3 Factors of 6x2 are 1, 2,3, 6, x, x2, 2x, 2x2 ,3x, 3x2 ,6x, 6x2 Factors of 4x are 1,2,4,x,2x,4x. Thus the GCD of the above terms is 2x. Dividing 2x3 , -6x2 and 4x by 2x, we get x2 - 3x + 2 Then the GCD becomes one factor and the quotient is the other factor. 2x3 – 6x2 + 4x = 2x .(x2 - 3x + 2) Therefore the factors of 2x3 – 6x2 + 4x are 2x and (x2 - 3x + 2) Thus, 2x3 – 6x2 + 4x = 2x .(x2 - 3x + 2) Factorization by grouping the terms of the expression: Grouping the terms of the expression in such a way that there are common factors among the terms of the groups so formed. Read More About Properties of Equality
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