Quadratics are considered to be among the most challenging concepts in Mathematics. The terms X² and 64 are perfect squares and they are subtracted. The terms present² and 16 are perfect squares and are being subtracted.Note that in the quadratic equation above: Identify the value of X given that X²-16=0 Solution The terms present are perfect squares and being subtracted.Special Product Method is used here since: This X =-7 Case 2: Difference of Two Squares Expression The middle term, 14X is two times the roots of the other terms. The first term is X² and the last term is 49 both X² and 49 are perfect squares whose roots are X and 7 respectively. Identify the value of X given that X²+ 14X +49=0 Solution Check whether the middle term is 2 times the product of the roots of the other terms.Check whether the first and the last term are perfect squares.You can do this using two special quadratics: The Special Product Method requires special cases that can be factored quicker. Thus, X=4 or X= -6 Solving Quadratic Equations by Factorizing Using the Special Product Method Therefore, the expression becomes X²- 4X +6X-24=0 Think of two factors, such that their product is -24 and their sum is 2. Next, write 11X in the product of 10 and 1.Īfter grouping, take out the common factor.Ĭompute the value of X given that X²+2X-24=0 Solution Then think of two factors of 10 that can add up to 11 Group the expression into two pairs that have a common factor and simplify like this:ĭepending on your selection of P and Q, you will factor out a constant on the second parenthesis, remaining with two identical expressions as shown in the example below: Example 1įind the value of X given 5X² + 11X +2= 0 Solution.Rewrite the expression as AX² + QX +PX +C.Think of two numbers, say Q and P such that QP= AC and Q+P= B.Suppose you are given a general equation AX² +BX + C Use this easy procedure in solving the equation by factorizing using the grouping method. Use the factoring by grouping method if you can't find the common factor for all the terms.įurther, by taking two terms at the same time, you can get something to divide the terms. This method involves arranging the terms into smaller groupings with common factors. Thus X = 1 or X =2/3 How to Solve a Quadratic Equation by Factoring Using Grouping Method You should then rewrite the function as 3X²+3X-2X-2= 0. Therefore,(2X +5)(X-2)= 0 where X = 2 or X = -5/2 Example 2Ĭalculate the value of X given that 3X²+X-2 =0 Solutionįind two integers whose product is AC= 3 ×-2=-6 Now we have the common parenthesis, which is X-2. Rewrite the expression as 2X²- 4X + 5x - 10 = 0 You can now select the pair that has the sum of B = 1. You should then draw a table on your working paper to come up with several pairs. Example 1įind the value of X given that 2X²+ X -10=0 Solutionįind two integers whose product AC= (2)×(-10)=-20. To illustrate this case, let's consider the following examples. Use grouping by pair to factor out the Greatest Common Factor (GCF) in the two terms to get a common parenthesis.Rewrite the function as a four term expression as below AX² + MX + NX + C.Identify two integers whose product is AC and sum is B.If the equation AX²+BX + C =0 and A≠1 you only need a little extra effort to find the factors using the product sum method. You should then select a pair that has sum -16. You can have a table with different values for different pairs. Identify a duo of integers whose product is 60 the pairs are listed below. You can then select the pair that has the sum of 16 and product 55. Illustration 1įind two integers whose product is 15. Step Three: Make one factor ( X + M ) and the other ( X + N). Step Two: Give the integers any characters of your choice, for example, M and N. Step One: Find two integers whose product is C. Simply follow these steps when solving an equation using the product sum method: Unlike the trial and error method, the Product Sum Method is generally easier to apply since it identifies an equation that cannot be factored. This method is mainly used by students who find it challenging to use the guessing method, (or the trial and error method). Use the Sum-Product Method in Solving Quadratic Equations by Factorizing There are, basically, three methods of solving Quadratic Equations by Factoring: Here's All You Need to Know About Solving Quadratic Equations by Factoring The standard form of any quadratic equation must be expressed as AX²+ BX + C≠0, where A, B, and C are values, except that A can't be equal to zero, and X is unknown (yet to be solved). This is because the variable gets squared(X²).Ī quadratic equation is, thus, sometimes referred to as Equation of Degree 2 since the greatest power is 2 (having one or more variables raised to the second power). The term "quadratic" traces from the Latin word "quad," which means "square."
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