How to Factor Monomials With Variables?

TopMonomial is an algebraic expression, in monomial “mono” means one, so we can say that polynomial containing single term is called as monomial. For example: 4x2, 4y, x, 7, here 'x' and 'y' are variables and 7, 4 are constant, so we can say that any single term is a monomial and multiplication of variable and constant is also called monomial, monomial should not have negative and fractional exponents like 4x 2/3, 4-2 etc. Monomial which contains two different variables is called monomial with two variables, for example 4xy , 34 x4 y5 etc. are called monomials.

Now we will see how to factor monomials with variables: Let’s take a monomial with 3 variable 28 x4 y5 z3, factor this monomial.

Solution: Here we can see that x ,y, z are three variable means we have three unknown values.
So first of all Set monomial equals to zero 28 x4 y5 z3 = 0,set this equals to zero because if we set this to anything else then it will change into another polynomial like binomial, trinomial etc. So to factor this monomial break down each term into its smallest factor, so here first of factor of 28 is: 28 = 2 * 2 * 7, factor of x4 = x * x * x * x, and factor of y5 = y * y * y * y * y, z3 = z * z * z. So factors are 2 * 2 * 7 * x * x * x * x* y * y * y * y * y * z * z * z.