Solving Quadratic Equations: In Factored Form

Common Core Grade Level: 
Packet includes: 
27 practice problems and an answer key.

This packet helps students understand how solve quadratic equations once they are already factored.  Once students get quadratic equations into factored form, it's quite easy to find the solutions (also called roots and x-intercepts).  

Quadratic equations can be factored into two binomials.  Because of the multiplicative property of zero, once of those binomials must equal zero, which allows students to determine the 1 or 2 possible values of x.  For example:

$x^2+4x+3=0$ can be factored into

$(x+3)(x+1)=0$

So, $x+3=0$ or $x+1=0$

The solutions of the equation are -3 and -1.

Students who need to practice factoring should see the note below.

Each page in this packet starts with easier problems that get more difficult as students work through the packet. After doing all 27 problems, students should be more comfortable doing these problems and have a clear understanding of how to solve them. 

Sample Problem(s): 

Solve for x.  

Simple:  

$0=(x+2)(x-1)$  

Advanced:  

$0=(2x+3)(3x+7)$ 

Notes: 

Practice problems require knowledge of addition, subtraction, multiplication, and division of integers.

Students who need to practice factoring quadratic expressions and equations (to get them to the factored form that they begin in in this practice packet) should do our Factoring Polynomials:$ax^2+bx+c$ practice packet.

Video lesson(s) showing you how to do this type of problem: 

Graphing Equations using Roots (This video shows how to factor and how to use factored form to find solutions)

Downloadable File(s): 
Solving Quadratic Equations in Factored Form.pdf
Solving Quadratic Equations in Factored Form Answer Key.pdf
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