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.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |