6 – 4 6 – 4 Factoring and SolvingFactoring and SolvingPolynomial EquationsPolynomial Equations

Day 2Day 2

Objective: Use factoring to solve polynomial equations.

Example 5

Solve 5 32 24 14x x x

5 3

5 3

4 2

2 2

2

2 24 14 Given

2 14 24 0

2 7 12 0

2 3 4 0

2 3 2 2 0

x x x

x x x

x x x

x x x

x x x x

2

2

2

2 3 2 2 0

2 0 or 3 0 or 2 0 or 2 0

0, 3 2 2

3

x x x x

x x x x

x x x x

x

The solutions are 0, 3, 2, and 2.

Example 5

An optical company is going to make a glass prism that has a volume of 15 cm3. The height of the prism is h cm, and the base will be a right triangle with legs of length (h – 2) and (h – 3) cm. What will be the height of the prism?

Solution

If a prism has a volume of V cubic units, a base with an area of B square units, and a height of h units, then

V = Bh

Base of a triangular prism is B = ½ leg1 x leg2

3

2

3 2

3 2

3 2

2

2

115 2 3

2

15 6

2

15 6

2

30 5 6

0 5 6 30

0 5 6 5

0 6 5

V Bh

cm h h h

h h h

h h h

cm h h h

h h h

h h h

h h

2

2

6 0 or 5 0

6 5

6

6

h h

h h

h

h i

Since distance cannot be an imaginary number the height must be h = 5 cm.

Homework page 348 28 –60 even, 75 – 85 odd