solving a quadratic equation by factoring

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. 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”.Step 1) Two numbers that multiply to give -30 and add to give 1 are 6 and -5.

Step 3) We factor the first two terms and write the second two terms separately: Step 1) We have to find two numbers whose product is 9 and whose sum is 6. Step 4) We factor the equation and solve: Step 3) We factor the first two terms and the second two terms separately: Step 2) We rewrite the quadratic equation as: Step 1) We look for two numbers whose product is 63 and whose sum is -16. Step 4) Factor the common term and set different factors equal to zero and solve for the variable.

Step 3) Factor the first two terms and the second two terms separately. The coefficients of the two terms are the two numbers found in Step 1). Step 2) Write the middle term, bx, as the sum of two terms. Step 1) Find two numbers whose product is equal to a c, and whose sum is equal to b. In order to factor a quadratic equation, one has to perform the following steps: A general quadratic equation is given by:

Permutations and Combinations Toggle Dropdownįactoring Quadratic Equations One way to solve a quadratic equation is by factoring the equation.

Mutually Exclusive and Non-Mutually Exclusive Events.

Solving Quadratic Equations by Completing the Square.

Solving Problems Involving Logarithmic Functions.

Solving Problems Involving Exponential Functions.

Logarithmic and Exponential Functions Toggle Dropdown.

Adding and Subtracting Rational Expressions.

Rational Expressions and Non-Permissible Values.

Rational Expressions and Equations Toggle Dropdown.

Solving a quadratic equation by factoring