quadratic equation by factoring examples

In these cases it is usually better to solve by completing the square or using the quadratic formula. However, not all quadratic equations can be factored evenly. (1,180) (2,90) (3,60) (4,45) (5,36) (6,30) ģ.2: p = -180, a negative number, therefore one factor will be positive and the other negative.ģ.3: b = 24, a positive number, therefore the larger factor will be positive and the smaller will be negative.įactoring quadratics is generally the easier method for solving quadratic equations. Is negative then one factor will be positive and the other negative. This equation is already in the proper form where a = 15, b = 24 and c = -12. Step 1: Write the equation in the general form ax 2 + bx + c = 0. This equation is already in the proper form where a = 4, b = -19 and c = 12.ģ.2: p = 48, a positive number, therefore both factors will be positive or both factors will be negative.ģ.3: b = -19, a negative number, therefore both factors will be negative. Step 8: Set each factor to zero and solve for x. Now that the equation has been factored, solve for x. Using the reverse of the distributive property we can write the outside expressions (shown in red in Step 6) as a second polynomial factor. When a quadratic equation is not factorable, another method is needed to solve for x. If this does not occur, regroup the terms and try again. Notice that the parenthetical expression is the same for both groups. Step 7: Rewrite the equation as two polynomial factors. Step 6: Factor the greatest common denominator from each group. Step 4: Rewrite bx as a sum of two x -terms using the factor pair found in Step 3.

Make sure all the words and ideas are understood. Here’s a problem-solving strategy to solve word problems: Step 1: Read the problem. There are problem solving strategies that will work well for applications that translate to quadratic equations. If p is negative and b is positive, the larger factor will be positive and the smaller will be negative.ģ.2: p = 12, a positive number, therefore both factors will be positive or both factors will be negative.ģ.3: b = 7, a positive number, therefore both factors will be positive. Solving Real-World Applications Modeled by Quadratic Equations. If p is positive and b is negative, both factors will be negative. If both p and b are negative, the larger factor will be negative and the smaller will be positive. If both p and b are positive, both factors will be positive. If p is negative then one factor will be positive and the other negative.ģ.3: Determine the factor pair that will add to give b. If p is positive then both factors will be positive or both factors will be negative. Step 3: Determine the factor pairs of p that will add to b.įirst ask yourself what are the factors pairs of p, ignoring the negative sign for now. c and find the factors of the result, let's call this p.This equation is already in the proper form where a = 3, b = 7 and c = 4. Factoring quadratic expressions Before starting any factoring problem, it is helpful to write your expression in standard form. Set each factor to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero).

Transform the equation using standard form in which one side is zero.

This method is similar to grouping to solve quadratic Equations, with a leading coefficient equal to 1.Step 1: Write the equation in the general form To solve an quadratic equation using factoring : 1 1. x 1 : 4 x = 0 x 1 = 0 x 2 : 3 x + 2 = 0 x 2 = - 2 3įactoring by taking out Common Factors can also be used. 4 x ( 3 x ) + 4 x ( 2 ) = 4 x ( 3 x + 2 ) = 0 Step 5 (solving the quadratic equation): Equate the factored expression to 0 and solve for the x-intercepts. 2 Step 3: Having rewritten your terms, rewrite your quadratic equation in the following form: a b + a c = 0 12 x 2 + 8 x = 4 x ( 3 x ) + 4 x ( 2 ) = 0 Step 4: Apply the law of distributive property and factor out your greatest common factor.You can determine the other factor by dividing your term by your GCF. Step 2: Write out each term as a product of the greatest common factor and another factor, i.e. x The Number and variables that appear the most are 4 and x, therefore making our GCF=4x.

Step 1: Find the greatest common factor by identifying the numbers and variables that each term has in common.

Quadratic equation by factoring examples