5.8:  Factoring Applications

What are some examples where factoring is used in life?

Word Problem:

Find the area of a rectangle given that the length of the rectangle is 5 more than twice the width.

Solution:

2x + 5

x

To find the area of a rectangle use the formula for Area of a rectangle:  Area = Length times Width or

In this case, the width is “x” and the length is “2x+5” so the area is:

Factoring Application 1:  Factoring can be used to find unknowns.

Example:

Find the length and width of a rectangle whose area is:       

(In this case, the length is the longer side and the width is the shorter side.)

Once the width and length algebraic expressions are found, find the value of the width and length when  x = 5 ft.  Then verify the area by substituting x = 5 ft into the area expression.

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Solution:

To find the solution factor the area to find the length and width:

The width is “x + 2” feet and the length “2x + 1” feet.

2x + 1

x + 2

If x = 5 ft, then:

Practice Example:

Find the length and width of a rectangle  garden whose area is:    

(In this case the length is the longer side and the width is the shorter side.)

Once the width and length are found, find the value of the width and length when  x = 10 ft.  Then verify the area by substituting x = 10 ft into the area.

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Practice Example:

Find the length and width of a square play area whose area is: 

(In this case the length is the longer side and the width is the shorter side.)

Once the width and length are found, find the value of the width and length when  x = 6 ft.  Then verify the area by substituting x = 6 ft into the area.

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Factoring Application 2:  Solving real life equations

The equation of a person who dives off a 48 ft. cliff into a river with an initial velocity of 32 ft/sec is:

,  where “t” is time in seconds and “h” is height in feet.

When will the diver hit the water (when height = 0)?

Solution:

To find the solution:

1)  Substitute 0 in for the height (h)

2)  Factor the trinomial by first factoring out the -16:

3)  Continue factoring by factoring the trinomial:

4)  Set each term with a variable equal to the right side of 0 and solve for t:

5)  The solutions are 3 seconds and -1 seconds.  Since -1 seconds is not realistic, we do not include that solution.  The diver will hit the water is 3 seconds.

Practice Example: 

The equation of a person who dives off a 64 ft. cliff into a river with an initial velocity of 0 ft/sec is:

,  where “t” is time in seconds and “h” is height in feet.

When will the diver hit the water (when height = 0)?

Practice Example: 

The equation of the path of a ball thrown in the air at a speed of 96 ft/sec is:  ,  where “t” is time (seconds) and “h” is height in feet.

When will the ball hit the ground (when height = 0)?

What are some examples where factoring is used in life?

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5.8:  Factoring Applications Practice Problems

Solve:

1.  Find the length and width of a rectangular room whose area is:

Draw a picture of the situation.

(In this case the length is the longer side and the width is the shorter side.)

Once the width and length are found, find the value of the width and length when  x = 10 ft.  Then verify the area by substituting x = 10 ft into the area.

2.  Find the length and width of a square room whose area is:

Draw a picture of the situation.

(In this case the length is the longer side and the width is the shorter side.)

Once the width and length are found, find the value of the width and length when  x = 4 ft.  Then verify the area by substituting x = 4 ft into the area.

5.8:  Factoring Applications Practice Problems Continue

Solve:

3. The equation of a person who dives off a 96 ft. cliff into a river with an initial velocity of 16 ft/sec is:

,  where “t” is time in seconds and “h” is height in feet.

When will the diver hit the water (when height = 0)?

4. The equation of the path of a ball thrown in the air at a speed of 16 ft/sec is:  ,  where “t” is time (seconds) and “h” is height in feet.

When will the ball hit the ground (when height = 0)?