warm up foil (3x+7)(x-1) factors, roots and zeros
TRANSCRIPT
Warm Up
Foil(3x+7)(x-1)
Factors, Roots and Zeros
Definition: Factoring
Terms are Factors if, when they are multiplied, they equal that poly
Example
(x - 3) and (x + 5) are Factors of the polynomial
𝐹𝑎𝑐𝑡𝑜𝑟 :𝑥2+2 𝑥−15
Answer: (x-3)(x+5)
22 15x x
Definition: Solutions or Roots
• The solutions to a poly are the points where the graph crosses the x-axis.
• Also called Roots or x-intercepts.• All the same thing!
• Solutions = Roots = x-intercepts
• Picture…
Graph of a Polynomial Function
Here is the graph of our polynomial function:
The Zeros of the Polynomial are the values of x when the polynomial equals zero. In other words, the Zeros are the x-values where y equals zero.
y x2 2x 15
Example f(x) = x2 - 4
Identifying Solutions4
2
-2
-4
-5 5
Solutions are -2 and 2.
Now you try this problem.
f(x) = 2x - x2
Solutions are 0 and 2.
Identifying Solutions
4
2
-2
-4
5
Try this problem y = x2 - 2x - 8.
Roots?Zeros?
Graphing Quadratic Equations
x y-2-1134
4
2
-2
-4
5