Factor Polynomials Factor Polynomials A polynomial is defined as the combination of values and the variables means when we talk about the polynomial equation then it is describes an expression that has the combination of constants , variables and the operations like addition and subtraction and multiplication and the variables also have the power that are always in a form of non negative Integer. It cannot be defined in terms of fraction or negative values. Factor of a polynomial m ( x ) is defined as another polynomial that divides the polynomial m ( x ) into evenly parts. To understand it we can take an example of a polynomial m ( x ) = x 2 – 4 9 a then the factor of that given polynomial is x + 2 that equally divides the polynomial. Factor of the polynomial is explained as product of its factor. We can understand it as in above example factor of the polynomial m ( x ) = x 2 – 4 is ( x + 2 ) then x 2 – 4 is also defined in terms of factorization as ( x – 2 ) . ( x + 2 ) .
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we learn how to Factor the Polynomial. First we start with the Binomials means the expressions that have the highest power 2 of the variables. Example : We have an equation as a2 - 16. In this equation both the terms are the squares of a and 4 respectively as a2 = a . a and 16 = 4 . 4. This type of problem is known as difference of two squares. These type of problems are solved by using two steps : Step no. ( 1 ) : Calculate the root of each square in the expression . Example : a2 - 16 = ( a . a ) - ( 4 . 4 ) Step no. ( 2 ) : Two binomials are factored as one with addition and second with subtraction as a2 - 16 = ( a + 4 ) ( a – 4 ) Here we take several examples of difference of the perfect square : ( x 2 - 36 ) = ( x + 6 ) ( x – 6 ) or ( y 2 - 81 ) = ( y + 9 ) ( y – 9 ) . Now when we have the expression of difference of the cubes of sum of the cubes then factors of these expressions are explained as ( a 3 – b 3 ) = ( a – b ) ( a 2 + a b+b2) (a3+b3)=(a+b)(a2–ab+b2)
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If the given expression is a quadratic function as an equation a 2 + 8 a + 15 then it is factorized as : -find two numbers that have the multiplication equal to the 15 and on adding they are equal to the 8 . So by factoring the 8 we get two numbers 5 . 3 = 15 and 5 + 3 = 8 So the factor of the equation a 2 + 8 a + 15 = ( a + 5 ) ( a + 3 ) .
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