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Here in the above polynomial, the middle term is split as the sum of two factors, and the constant term is expressed as the product of these two factors. Consider the quadratic polynomial of the form x 2 + x(a + b) + ab. The general form of a quadratic equation is x 2 + x(a + b) + ab = 0, which can be split into two factors (x + a)(x + b) = 0. Further, the quadratic equation has to be factorized to obtain the factors needed for the higher degree polynomial. While factoring polynomials we often reduce the higher degree polynomial into a quadratic expression. The process of factoring polynomials is often used for quadratic equations. 8ab + 8b + 28a + 28 = 4(2b + 7)(a + 1) Factoring Polynomials by Splitting Terms Thus the factoring polynomials is done by grouping. Let us group 2ab+2b and 7a+7 in the factor form separately.Ģab + 2b = 2b(a + 1), and 7a + 7 = 7(a + 1)
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Notice that 4 is a single factor common to all the terms of this polynomial. Let us solve an example problem to more clearly understand the process of factoring polynomials. Let us try to understand grouping for factorizing with the help of the following example. First, we split each term of the given expression into its factors and further aim at taking common terms to find the group of factors. The number of terms of the polynomial expression is reduced to a lesser number of groups. Here we aim at finding groups from the common factors, to obtain the factors of the given polynomial expression. The method of grouping for factoring polynomials is a further step to the method of finding common factors. 3īy distributive law, 3x+9= 3.x + 3.3 = 3(x+3) Factoring Polynomials By Grouping Let us understand this better with the help of an example.īy factoring each term we get, 3 x + 3. This is equivalent to using the distributive property in reverse.
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Further, the common factors across the terms are taken to obtain the possible factors. As a first step, the factors of each of the terms of the algebraic expression are written. This is the simplest method of factoring an algebraic expression by taking common factors of each of the terms of the given expression. Let us discuss each of the methods of factoring polynomials. The four important methods of factoring polynomials are as follows. The method of factorization depends on the degree of the polynomial and the number of variables included in the expression. There are numerous methods of factoring polynomials, based on the expression.
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