Lesson 4 Contents
Lesson 4 Contents
Example 1Factor ax2 + bx + cExample 2Factor When a, b, and c
Have a Common FactorExample 3Determine Whether a Polynomial Is
PrimeExample 4Solve Equations by FactoringExample 5Solve Real-World
Problems by Factoring
Example 4-1a
Write the pattern.
Group terms with common factors.
Factor the GCF from each grouping.
andAnswer:
Distributive PropertyCheckYou can check this result by
multiplying the two factors.FOIL methodFOIL
Simplify.
Example 4-1a
Factor
Answer:
The correct factors are 4, 18.Example 4-1b
Factor
In this trinomial,and Since b is negative, is negative. Since c
is positive, mn is positive. So m and n must both be negative.
Therefore, make a list of the negative factors of or 72, and look
for the pair of factors whose sum is 22.
733827221, 722, 364, 244, 18Sum of FactorsFactors of 72
Example 4-1b
Write the pattern.
and
Group terms with common factors.
Factor the GCF from each grouping.
Distributive PropertyAnswer:
Example 4-1b
a. Factorb. Factor
Answer:
Answer: Example 4-2a
961, 82, 4Sum of FactorsFactors of 8
Factor
Notice that the GCF of the terms, and 32 is 4. When the GCF of
the terms of a trinomial is an integer other than 1, you should
first factor out this GCF.
Distributive PropertyNow factorSince the lead coefficient is 1,
find the two factors of 8 whose sum is 6.
The correct factors are 2 and 4.
Example 4-2a
Answer: So,Thus, the complete factorization ofis
Example 4-2b
Factor
Answer:
Example 4-3a
1414221, 151, 153, 53, 5Sum of FactorsFactors of 15Factor
In this trinomial,and Since b is positive, is positive. Since c
is negative, mn is negative, so either m or n is negative, but not
both. Therefore, make a list of all the factors of 3(5) or 15,
where one factor in each pair is negative. Look for the pair of
factors whose sum is 7.
Example 4-3a
There are no factors whose sum is 7. Therefore, cannot be
factored using integers.
Answer:is a prime polynomial.
Example 4-3b
Factor
Answer: prime Example 4-4a
Solve
Original equation
Rewrite so one side equals 0.
Factor the left side.
orZero Product Property
Solve each equation.
Answer: The solution set is Example 4-4b
Solve
Answer:
Example 4-5a
Model Rockets Ms. Nguyens science class built an air-launched
model rocket for a competition. When they test-launched their
rocket outside the classroom, the rocket landed in a nearby tree.
If the launch pad was 2 feet above the ground, the initial velocity
of the rocket was 64 feet per second, and the rocket landed 30 feet
above the ground, how long was the rocket in flight? Use the
equation
Example 4-5a
Vertical motion model
Subtract 30 from each side.
Factor out 4.
Divide each side by 4.
Factor
orZero Product Property
Solve each equation.
Example 4-5a
The solutions areandseconds. The first time represents how long
it takes the rocket to reach a height of 30 feet on its way up. The
second time represents how long it will take for the rocket to
reach the height of 30 feet again on its way down. Thus the rocket
will be in flight for 3.5 seconds before coming down again.
Answer: 3.5 seconds Example 4-5b
When Mario jumps over a hurdle, his feet leave the ground
traveling at an initial upward velocity of 12 feet per second. Find
the time t in seconds it takes for Marios feet to reach the ground
again. Use the equation
Answer: second
End of Lesson 4
