methods for factoring quadratic equations

We will create our factor pairs using factors of -18. This is why this is called the ac method. Before we begin factoring, we will determine the value of ac. We are now ready to build our tower higher and factor the more difficult equations. Just as builders must start construction with a strong foundation, our foundational knowledge of factoring prepares us for greater challenges. Do not worry! Having a great understanding of the simpler method will make this approach very manageable. We can verify by creating the graph of y=x^2-8x-20.Īs promised, we can now demonstrate the more difficult cases where a e 1. Therefore, the two x-intercepts of the equation y=x^2-8x-20 are at 10 and -2. When we set both factors equal to zero, we obtain two equations: x-10=0 and x+2=0. To solve for the value(s) of x, we will set each factor equal to 0. The factor pair -10 and 2 multiplies to -20 and adds to -8. We will only include such factor pairs in the table below. This means the number with the larger absolute value in the factor pair must be *negative*. We also know the numbers must add up to a negative number. We know the factors must have opposite signs because a positive multiplied by a negative will produce a negative number. The sum should add up to b, in this case -8. Again, there are many possible factor pairs. To factor the expression x^2-8x-20, we must first determine the factors of c (in this case -20).

Let’s determine the roots (or x-intercepts) of the equation: Return to the Table of Contents Solving y=x^2-8x-20 We can verify by creating the graph of y=x^2+7x+12. Therefore, the two x-intercepts of the equation y=x^2+7x+12 are at -3 and -4. When we set both factors equal to zero, we obtain two equations: x+3=0 and x+4=0. This is because we know that anything multiplied by 0 is 0. Remember, (x+3) is being multiplied with (x+4). To solve for the value(s) of x, we must set each factor equal to 0. Therefore, we can factor x^2+7x+12=0 into: The factor pair 4 and 3 multiplies to 12 and adds to 7. Let’s make a table determining the sum of all the ways to factor 12. The sum should add up to b, in this case 7. To determine which factors to use, we must also determine the sum of the factors. There are many ways 12 can be factored, such as using -12 and -1 or using 6 and 2. To factor the expression x^2+7x+12, we must first determine the factors of c, in this case 12. Now, let’s solve for the x-intercepts by factoring. To start, let’s try solving the equation: But no need to worry, we include more complex examples in the next section. We simply must determine the values of r_1 and r_2. In these cases, solving quadratic equations by factoring is a bit simpler because we know factored form, y=(x-r_1)(x-r_2), will also have no coefficients in front of x.

$methods for factoring quadratic equations$

If a=1, then no coefficient appears in front of x^2. Remember, the standard form of a quadratic is:įor more information about forms of quadratics, check out our article on the different forms of quadratics. For our purpose, a simple quadratic means a quadratic where a=1. The x-intercepts can also be referred to as zeros, roots, or solutions. When you are asked to “solve a quadratic equation”, you are determining the x-intercepts. Return to the Table of Contents Factoring Quadratic Equations Examplesīefore things get too complicated, let’s begin by solving a simple quadratic equation. …we are simply saying that when we multiply (x-r_1) and (x-r_2), we will get the product ax^2+bx+x. Likewise, when we factor the standard from of a quadratic equation: Factors are terms that, when multiplied together, produce the original number or expression.Factoring a number or expression means breaking it into separate factors.There are other ways to factor 12, as well, such as using the factors 4 and 3 instead. The numbers 6 and 2 are factors of 12 because multiplying 6 and 2 gives the product of 12. Solving a Quadratic Equation Using Completing the Squareīefore we dig deep into factoring quadratic equations, let’s remember what factors are by looking at numerical examples.Determine a Quadratic Equation Given Its Roots.Solving Quadratic Equations by Factoring: World Problems.Factoring Trinomial with The Box Method.Video Examples of Factoring Quadratic Equation.Solving Quadratic Equations with the “AC Method”.

Methods for factoring quadratic equations