#Solving quadratic equation by factoring how to#

Step 2: Rewrite the equation with the substitution to put it in quadratic form. Solution: Step 1: Identify a substitution that will put the equation in quadratic form.

#Solving quadratic equation by factoring how to#

However, not all quadratic equations can be factored evenly. Example 9.4.1 How to Solve Equations in Quadratic Form. If your equation isnt set equal to 0, just move everything over to. You cant use the Zero Product Property if its not set equal to 0. If youre going to solve a quadratic equation with this method, the first thing you need to do is make sure the equation is set equal to 0. (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. Not all quadratic equations look the same as the example we just had. The algebraic common factor is x in both terms. The numerical factor is 3 (coefficient of x 2) in both terms. Consider this quadratic equation: 3x 2 + 6x 0. Is negative then one factor will be positive and the other negative. Let us solve an example to understand the factoring quadratic equations by taking the GCD out. 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. 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. Explanation: This is a factoring problem, so we need to get all of the variables on one side and set the equation equal to zero. Step 4: Rewrite bx as a sum of two x -terms using the factor pair found in Step 3. 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.

If you need a reminder on how to factor, go back to the section on: Factoring Trinomials. For the time being, we shall deal only with quadratic equations that can be factored (factorised). If p is positive and b is negative, both factors will be negative. Solving a Quadratic Equation by Factoring. 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. When solving quadratic equations by factoring, the first step is to put the equation in standard form ax2 + bx + c 0, equal to zero. 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. Consider the following example.Step 1: Write the equation in the general form However, the coefficients of the obtained factors might no longer be integers. Some trinomials can be factored using other methods, like the Difference of Squares formula.

The above trinomial cannot be factored at all. When a pair of integers whose product is equal to a ⋅ c and whose sum is b cannot be found, the trinomial cannot be factored using the described method. Please note that not every quadratic trinomial can be factored. Sometimes such expressions can be factored using the Difference of Squares formula.

A quadratic trinomial is of the form a x 2 + c when b is equal to 0.

To write this expression in factored form, the GCF of a x 2 and b x has to be factored out.

A quadratic trinomial is of the form a x 2 + b x when the constant term c is equal to 0.

However, in these two cases there are other approaches that might be used as well. It is particularly useful for trinomials in the forms a x 2 + b x or a x 2 + c. The above method can be used to factor any quadratic trinomial.