The document discusses factoring polynomials using the difference of squares pattern and perfect square trinomial pattern. It provides examples of factoring expressions involving these patterns, including solving polynomial equations. The examples illustrate factoring expressions with variables and evaluating expressions to solve vertical motion problems.
12. Example 5
Solve a vertical motion problem
FALLING OBJECT
A window washer drops a wet sponge from a height of
64 feet. After how many seconds does the sponge land
on the ground?
SOLUTION
Use the vertical motion model to write an equation for
the height h (in feet) of the sponge as a function of the
time t (in seconds) after it is dropped.
Because the sponge was dropped, it has no initial
vertical velocity. To determine when the sponge lands
on the ground, find the value of t for which the height is
0.
13. Example 5
Solve a vertical motion problem
h = β 16t2 + vt + s
Vertical motion model
0 = β 16t2 + ( 0 ) t + 64
Substitute 0 for h, 0 for v, and
64 for s.
0 = β 16 ( t2 β 4 )
Factor out β 16 .
0 = β 16 ( t + 2 ) ( t β 2 )
Difference of two squares pattern
t + 2 = 0
or
t = β2
or
t β 2 = 0
t = 2
Zero-product property
Solve for t.
Disregard the negative solution of the equation.
14. Example 5
Solve a vertical motion problem
ANSWER
The sponge lands on the ground 2 seconds after it is
dropped.