Objective
The student will be able to:
1. solve a polynomial in factored form
2. relate factors and x-intercepts
How do we get zero?
When we multiply two numbers together
and the answer is zero, what MUST be
true?
One of the numbers MUST be zero!!!
Zero Product Property
If a • b = 0 then
a=0,
b=0,
or both a and b equal 0.
1. Solve (x + 3)(x - 5) = 0
Using the Zero Product Property,
you know that either
x + 3 = 0 or x - 5 = 0
Solve each equation.
x = -3 or x = 5
{-3, 5}
2. Solve (2a + 4)(a + 7) = 0
2a + 4 = 0 or a + 7 = 0
2a = -4 or a = -7
a = -2 or a = -7
{-2, -7}
3. Solve (t + 5)2 = 0
(t + 5)2 = (t + 5)(t + 5) = 0
t + 5 = 0 or t + 5 = 0
t = -5 or t = -5
{-5}
But
they’re the
same!
4. Solve (3x + 2)(4x + 3)(x + 4) = 0
(3x + 2)(4x + 3)(x + 4) = 0
3x + 2 = 0 or 4x + 3 = 0 or x + 4 = 0
3x = -2 or 4x = -3 or x = -4
x = -2/3 or x = -3/4 or x = -4
{-2/3, -3/4, -4}
4. Solve
Greatest
Common
Factor
2
x
- 11x = 0
GCF = x
x(x - 11) = 0
x = 0 or x - 11 = 0
x = 0 or x = 11
{0, 11}
Solve (y – 3)(2y + 6) = 0
1.
2.
3.
4.
{-3, 3}
{-3, 6}
{3, 6}
{3, -6}
x-intercepts and factors
Why are we learning this???
x-intercepts = where the graph crosses
the x-axis.
The value of y at this point is always zero.
Factors make graphing easier!!!
5. Sketch the graph of y = (x – 4)(x + 2)
Set the factors equal to zero and solve.
(x – 4)(x +2) = 0
x – 4 = 0 or x + 2 = 0
x = 4 or x = -2
{-2, 4}
These are the x-intercepts!
y = (x – 4)(x + 2)
Now find the coordinates of the vertex
(take the average of the intercepts)
x=1
Substitute x to find the y-coordinate
y = (1 – 4)(1 + 2)
y = -9
vertex = (1, -9)
Graph it!
y = (x – 4)(x + 2)
Homework
p600 #19 – 33 (15 problems)
EXTRA CREDIT OPPORTUNITY – Turn
in the correct answer to Mrs. Portz by
4/27/09 for 5 extra credit points.
Maria told this puzzle to her friends. “The
product of four times my age and 45 less
than three times my age is zero. How old
am I?” Find Maria’s age.
Let m = Maria’s age.
EXTRA CREDIT OPPORTUNITY – Turn
in the correct answer to Mrs. Portz by
4/27/09 for 5 extra credit points.
Find two consecutive integers
whose product is 240.
Let n = 1st integer.
Let n + 1 = 2nd integer.