2/24/2024 0 Comments Factorize quadratic equations![]() Verify by substituting the roots in the given equation and check if the value equals 0. Consider the quadratic equation x 2 + 5x + 6 = 0 Let us go through some examples of factoring quadratics:ġ. Hence, factoring quadratics is a method of expressing the quadratic equations as a product of its linear factors, that is, f(x) = (x - \(\alpha\))(x - \(\beta\)). ![]() Thus, (x - \(\beta\)) should be a factor of f(x). Similarly, if x = \(\beta\) is the second root of f(x) = 0, then x = \(\beta\) is a zero of f(x). Thus, (x - \(\alpha\)) should be a factor of f(x). ![]() This means that x = \(\alpha\) is a zero of the quadratic expression f(x). Suppose that x = \(\alpha\) is one root of this equation. Consider a quadratic equation f(x) = 0, where f(x) is a polynomial of degree 2. They are the zeros of the quadratic equation. Every quadratic equation has two roots, say \(\alpha\) and \(\beta\). The factor theorem relates the linear factors and the zeros of any polynomial. Factorization of quadratic equations can be done using different methods such as splitting the middle term, using the quadratic formula, completing the squares, etc. This method is also is called the method of factorization of quadratic equations. = (5 + x)(5 - x) Ĭlick here to find more information on quadratic equations.Factoring quadratics is a method of expressing the quadratic equation ax 2 + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax 2 + bx + c = 0. ![]() This is because a² - b² = (a + b)(a - b). If you are asked to factorise an expression which is one square number minus another, you can factorise it immediately. Unfortunately, the only other method of factorising is by trial and error. It is worth studying these examples further if you do not understand what is happening. Once you work out what is going on, this method makes factorising any expression easy. We need to split the 2x into two numbers which multiply to give -8. Now, make the last two expressions look like the expression in the bracket: ![]() The first two terms, 12y² and -18y both divide by 6y, so 'take out' this factor of 6y.Ħy(2y - 3) - 2y + 3 One systematic method, however, is as follows: There is no simple method of factorising a quadratic expression, but with a little practise it becomes easier. This video shows you how to solve a quadratic equation by factoring. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1). The first step of factorising an expression is to 'take out' any common factors which the terms have. This is an important way of solving quadratic equations. 2 x( x + 3) = 2x² + 6x ).įor an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.įactorising is the reverse of expanding brackets, so it is, for example, putting 2x² + x - 3 into the form (2x + 3)(x - 1). This section shows you how to factorise and includes examples, sample questions and videos.īrackets should be expanded in the following ways:įor an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket (e.g. ![]()
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