Transcript 6-4 Factoring and Solving Polynomial Equations (Day2)
6 – 4 Factoring and Solving Polynomial Equations Day 2
Objective: Use factoring to solve polynomial equations.
Example 5 Solve 2 2
x
5
x
5 24
x
14
x
3 24
x
14
x
3 Given 2 2 2 2
x
5 4 2 2 14
x
3 7
x
3 3 2
x
2 24 12
x
4 0 0 0
x
2
x
2 0
2 2 3
x
2
x
2 0 2
x
0 or
x
2 0 or
x
0 or
x x
0,
x
2 3
x
2
x
2
x
3 0
Example 5 An optical company is going to make a glass prism that has a volume of 15 cm 3 . 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 leg 1 x leg 2
V
Bh
15
cm
3 1 2
h
2
h
3
h
1 2
h
2 5
h
6
h
30
cm
1 2
h
3
h
3 5
h
2 5
h
2 6
h
6
h
0 0 0
h
3 5
h
2
h
2
h
2
h
6 6
h h
5 30
h
5
h
2
0 or
h h
2
6
h
5
h
6
h
i
6 0
Since distance cannot be an imaginary number the height must be h = 5 cm.
Homework page 348 28 –60 even, 75 – 85 odd