Transcript EQ: How is knowing the zero product property

EQ: How is knowing the zero
product property helpful when
solving equations by factoring?
1. 16x4 – 36x2y2
2. 20a2 – 7a – 6
3. 6t3 – 21t2 – 45t
4. 4n3 – 20n2 – 9n + 45
5. The area of a rectangle is: 20a2
– 13a – 15. Find the dimensions.
Factor.
I’ve Got the Answers:
1.
2.
3.
4.
5.
4x2 (2x – 3y) (2x + 3y)
(4a – 3) (5a + 2)
3t (t – 5) (2t + 3)
(n – 5) (2n – 3) (2n + 3)
(5a + 3) by (4a – 5)
Lesson 10-6
Solving Equations by
Factoring
Now that we know how to factor, we
can use factoring to solve
polynomial equations with one
variable such as:
k2 - 9k = -18
You can use the zero product
property to solve equations by
factoring.
Zero Product Property:
For all numbers a and b, if a*b = 0,
then a = 0, b = 0, or both a and b
equal 0.
If a product equals zero, at least one
of the factors has to equal zero.
Solve:
2
k
- 9k = -18
So, we try to get the polynomial to
equal zero.
In our example, that means adding 18
to both sides, so that there is nothing
left (or zero) on the other side.
Now, we have:
k2 – 9k + 18 = 0
Find the Factors…
Factor pairs are: 18 and 1,
9 and 2,
6 and 3
Let’s try -3 and -6
Sum
-3 + -6 = -9
(fits with middle term)
Product -3 * -6 = 18
(fits with last term)
k
k
k2
18
The equation factors to: (k – 3) (k – 6)
We will set each of the factors equal to zero to
find the solution. (k – 3) = 0 or k – 3 = 0
After solving, k = 3
The other factor (k – 6) also needs to be set
equal to zero and solved.
k–6=0
So, k =6.
There are 2 solutions (which should be
written in a solution set)  {3, 6}
Let’s try one more: 2x3 – 11x2 = 6x
Step 1: Get everything on one side.
2x3 – 11x2 – 6x = 0
Step 2: Remove any common factors.
x (2x2 – 11x – 6) = 0
Step 3: Continue factoring if possible.
Factors of 6:
6 and 1
3 and 2
2x
x 2x2
-6
We are going to be multiplying one of the
factors by two in order to get 2x2 for our
first term.
Last term is negative, so we need one
positive and one negative factor.
- 6 * 2 = - 12
+ 1
- 11
2x + 1
x 2x2 1x
- 6 -12 - 6
Our final factoring:
x (2x + 1) (x – 6) = 0
Don’t forget the GCF
you factored out
So, x = 0, 2x + 1 = 0,
x–6=0
Solution set {-½, 0, 6}
Practice, Practice, Practice!!
1. x2 + 64 = 16x
x2 – 16x + 64 = 0
(x – 8)(x – 8) = 0
x={8}
2. 7n2 = 35n
7n2 – 35n = 0
7n (n – 5) = 0
n = { 0, 5 }
3. 5g + 6 = -g2
g2 + 5g + 6 = 0
(g + 3) (g + 2) = 0
g = { -2, -3 }
4. x2 - 4x - 21 = 0
(x – 7) (x + 3) = 0
x = { -3, 7 }
Any Questions??
This is the Last Lesson
in the Chapter…
Start Studying!!!