Use your knowledge and skills to help others succeed.ĭon't be wasteful protect our environment. Please include it as a link on your website or as a reference in your report, document, or thesis.Īlgebra topics Solving Quadratic Equations by Factoring (Notice: The School for Champions may earn commissions from book purchases) In such a case, you can try to solve the equation by the completing the square method or by using the quadratic equation formula. Some quadratic equations are not readily factored. Each factor can then be set to 0 and solved for x. The method requires that you first put the equation in the form of ax 2 +īx + c. For example, the first expression in the equation x 2 + 8x + 15 = 0 can be factored into (x + 3)(x + 5), and then those two factors can then be readily solved for x. You can find the solutions, or roots, of quadratic equations by setting one side equal to zero, factoring the polynomial, and then applying the Zero. One method of solving a quadratic equation is by factoring it into two linear equations and then solving each of those equations. This algebra video tutorial explains how to solve quadratic equations by factoring in addition to using the quadratic formula. In such a case, you can try solving by the Completing the Square method or the Quadratic Formula method. You really can't factor x 2 − 5x + 3 with rational numbers. There are some quadratic equations where solving by factoring is not effective. X = −2 When solving by factoring does not work You can factor the expression 2x 2 − 3x − 14 into (2x − 7)(x + 2). Since (x + 3)*0 = 0 and 0*(x + 5) = 0, you can set both expressions equal to zero and solve:Īnother example of solving by factoring is the equation: Seeing that 3 * 5 = 15 and 3 + 5 = 8, you can factor the expression x 2 + 8x + 15 into (x + 3)(x + 5). Set each expression equal to 0 and solve them for x to get our two solutions:Ĭonsider the quadratic equation x 2 + 8x + 15 = 0. The standard form of a quadratic equation of one variable is ax 2 +įactoring the quadratic expression ax 2 + bx + c consists of breaking the expression into two sub-expressions in the form of (dx + e)(fx + g).
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