1. 6.4 Solving by Factoring

2. Factor

3. Theorem
For all real numbers a and b, if and only if: or

4. So, if we change #1 to and factor, how can we use this theorem to find the possible values of x?

5. Sometimes a polynomial has two or more factors that are identical, we can call this solution a
or root.
When solving polynomial equations, first set the equation equal to using inverse operations (get everything to one side). Then, the equation and set each factor equal to and solve.
double
multiple
zero
factor
zero

6. Solve.

7. Solve.

8. Solve.
7. 8.

9. Applications
1. A manufacturer uses 1400 cm2 of cardboard to make a box with rectangular sides. If the box has a square base and a height of 30 cm, what is the volume of the box?

10. Applications
2. The area of a rectangle is 480 cm2. Its length is 4 cm more than 3 times the width. Find the dimensions of the rectangle.

11. Applications
3. The longer leg of a right triangle is 1 cm shorter than twice the shorter leg. The hypotenuse has length 1 cm longer than twice the shorter leg. Find the length of the three sides of the triangle.