Transcript 10.4 – Factoring to solve Quad. Goals / “I can…”

10.4
Factoring to solve Quadratics
10.4 – Factoring to solve Quad.
Goals / “I can…”
Solve quadratic equations by factoring
10.4 – Factoring to solve Quad.
So far we’ve found 2 ways to solve
quadratic functions
Graphing
Square Roots
10.4 – Factoring to solve Quad.
2
y = x – 4x – 5
Solutions are
-1 and 5
10.4 – Factoring to solve Quad.
Solve 4z2 = 9.
SOLUTION
4z2 = 9
Write original equation.
9
z2 = 4
Divide each side by 4.
9
z = ±
4
Take square roots of each side.
z=± 3
2
Simplify.
10.4 – Factoring to solve Quad.
Example 1
2
Example 2
2
x = 49
(x + 3) = 25
x2  49
( x 3)2
x=±7
x+3
x+3=5
Example 3
2
x – 5x + 11 = 0
This equation is
 25 not written in
the
=±5
x + 3 = –5 correct form to
use this
method.
x = 2 x = –8
10.4 – Factoring to solve Quad.
If I have 2 numbers and multiply them
together, and the product is zero, what
are the two numbers?
10.4 – Factoring to solve Quad.
One of them must be zero.
10.4 – Factoring to solve Quad.
Zero Product Property –
For every real number a and b, if ab = 0
then
a = 0 or b = 0.
10.4 – Factoring to solve Quad.
So if I have
(x + 4)(x + 5) = 0
then either
(x+ 4) = 0
or
(x + 5) = 0
10.4 – Factoring to solve Quad.
Example 1
2
x – 2x – 24 = 0
(x + 4)(x – 6) = 0
x+4=0 x–6=0
x = –4
x=6
Example 2
2
x – 8x + 11 = 0
2
x – 8x + 11 is
prime; therefore,
another method
must be used to
solve this equation.
10.4 – Factoring to solve Quad.
Example:
Given the equation, find the solutions
(zeros)
(x + 7)(x – 4) = 0
(2x + 3)(6x – 8) = 0
10.4 – Factoring to solve Quad.
So, if you have a trinomial equal to
zero, you can factor it to find the zeros.
10.4 – Factoring to solve Quad.
Example:
2
x + x – 42 = 0
2
3x – 2x = 21
10.4 – Factoring to solve Quad.
Story Problem:
Suppose that a box has a base with a
width of x, a length of x + 2 and a height
of 3. It is cut from a square sheet of
2
material with an area of 130 in . Find
the dimensions of the box.
10.4 – Factoring to solve Quad.
What we have is this:
3
3
x+2
x