An equation in mathematics is a relation that shows the equality between the variables and constants. An equation can be identity equation or inconsistent equation or conditional equation. An identity equation is satisfied by all possible values of the variables. A conditional statement is the one which has a restricted Set of values of the variables satisfying the given equation. For example, 4x + 8 = 12, Here only x = 1 can be the only possible value satisfying the equation. Last is the inconsistent equation that has no solutions. The number of terms in the equation determines the type of the equation like if we have 2 terms in the equation, then it is called as a binomial equation and so on. Let us learn how to factor an equation with 2 terms considering some examples of it:
Example 1: Suppose we have a binomial equation as: 4x2 – 8 x = 0, then what is the value of 'x'?
Solution: In the given equation we have to factorize the left hand side of the equation to get the value of 'x' as follows:
4x2 – 8x = 0,
Or 4x (x – 2) = 0,
Or x (x – 2) = 0,
Or x = 0 and x – 2 = 0,
Or x = 1 and x = 2,
Here we notice that for an equation of degrees 2 of the variable, we get two possible answers or values of the variable. Likewise we get more number of solutions for higher degrees of variables.
Example 2: Suppose we have an equation as: 5x3 + 125x2 = 0. Then what is the value of 'x'?
Solution: The given equation contains two terms on the left side and has to be factored:
5x2 (x + 25) = 0,
Or x2 = 0 and x = -25,
Or x = 0, x =0 and x = -25.