Solving Equations by Factoring
Steps to solve an equation by factoring:
Step 1: Bring all the terms to one side and set the equation equal to zero.
Step 2: Using the method of solving by factoring, take out the common terms and use one of the methods of factoring to simplify the expression.
Step 3: Once in this multiplication form, note that if two terms multiplied equal zero, one of the terms must be equal to zero. Given the rational roots theorem, these are the solutions to the equation.
Solve the following equation by factoring:
x2-7x=-6
x2-7x+6=0
(x-6)(x-1)=0
The solutions are x=1 and x=6
Solve the following equation by factoring:
16x
3+32x
2=9x+18
16x
3+32x
2-9x-18=0
16x
2(x+2)-9(x+2)=0
(x+2)(16x
2-9)=0
(x+2)(4x+3)(4x-3)=0
The solutions are x=-2, x=, x=
Solve the following equation by factoring:
27x
4=8x
27x
4-8x=0
x(27x
3-8)=0
x(3x-2)(9x
2+6x+4)=0
Since we cannot find any solution of 9x
2+6x+4, we can say that the solutions of the original equations are x=0 and x=
