Lesson 4: 3-4 Solving Quadratic Equations by Factoring

1. Which FOIL terms do you multiply to get like terms?
2. Which terms do you multiply to get the squared term?
3. Which terms do you multiply to get the constant term?
4. How can reformatting multiplication of binary terms this way help you factor quadratic equations?

Factored Form
FOIL Method

N.CN.8 Extend polynomial identities to the complex numbers.
A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

SAT questions related to solving quadratics: 2-3-13,3-3-14,1-3-16,5-3-3,8-3-16,1-4-25; analyzing graphs: 3-4-12,8-3-11,8-4-19,6-3-11

Quadratic equations can be solved using several different methods. Factoring can be a quick method. Once a polynomial has been factored, the Zero Product Property may be used to find the roots of the equation. If the polynomial is difficult to factor or is not factorable, then other methods must be used.

The factored form of a quadratic equation is 0=a(x-p)(x-q). In the equation, p and q represent the x-intercepts of the graph of the equation. In this lesson, you will learn how to change a quadratic equation in factored form into standard form and vice versa.

Some students may suggest solving a quadratic equation by dividing by the variable on both sides. This cannot be done because the value of the variable could be zero, and division by zero is undefined.

Provide each student with a sheet of grid paper. Have students begin by drawing a coordinate grid with two points on the x-axis plotted as the roots of a quadratic equation. Ask students to draw several parabolas that might be the graphs of different equations having those two points as their solutions. Point out that this demonstrates that the steps shown yield just one of the possible equations having the given roots.

McGraw Hill resources

McGraw Hill resources