Why factor quadratic equations

To solve this equation, we use the zero-product property. Set each factor equal to zero and solve. We can see how the solutions relate to the graph in Figure 2. The numbers that add to 8 are 3 and 5.

Then, write the factors, set each factor equal to zero, and solve. Recognizing that the equation represents the difference of squares, we can write the two factors by taking the square root of each term, using a minus sign as the operator in one factor and a plus sign as the operator in the other.

Solve using the zero-factor property. When the leading coefficient is not 1, we factor a quadratic equation using the method called grouping, which requires four terms. Factor the first two terms, and then factor the last two terms. This equation does not look like a quadratic, as the highest power is 3, not 2.

Recall that the first thing we want to do when solving any equation is to factor out the GCF, if one exists. And it does here. Skip to main content.

Quadratic Equations. Factoring quadratics is also done by using a formula that gives us the roots of the quadratic equation and hence, the factors of the equation. Then we find the value of x by using the formula:. By determining the factors, we can get the roots of the quadratic equation and hence the solution. The methods to factorize quadratic equations are splitting the middle term, using algebraic identities, using the quadratic formula, and factoring the GCD out.

Splitting the middle term and using the quadratic formula are the most efficient methods for factoring quadratic equations. When we factorize a quadratic equation , we get linear factors that divide the quadratic polynomial evenly.

The next step is finding the zeros of the equation by equating the factors with zero. Find the sum of the roots and the product of the roots or by identifying any known algebraic identity, we can factorize the quadratic equations.

There are different methods that can be used for factoring quadratic equations and solving the quadratic equations. Taking the common factors out, we can factorize quadratic equations easily. Learn Practice Download. Factoring Quadratics Factoring quadratics is a method of expressing the polynomial as a product of its linear factors. What is Factoring Quadratics? Methods of Factoring Quadratics 3. Identities for Factoring Quadratics 4.

So when you are presented with a quadratic equation, you know that the coefficient of the x term is the negative of the sum of the two roots and the constant coefficient is the product of them. This knowledge is usually a help in seeing if you can easily factor a quadratic.

By factorising first and then applying the multiplication property of zero, we can solve a quadratic equation. Since we can't know which one is the 0 , we consider each in turn being 0. So to apply this concept in solving a quadratic or cubic, quartic, etc equation, start by factorising to find the factors. Then let each factor be equal to 0 and solve to find the possible values of the variable. By factorising first and then applying the multiplication property of zero, we can solve the quadratic equation.