warm up foil (3x+7)(x-1) factors, roots and zeros

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Warm Up Foil (3x+7)(x-1)

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Page 1: Warm Up Foil (3x+7)(x-1) Factors, Roots and Zeros

Warm Up

Foil(3x+7)(x-1)

Page 2: Warm Up Foil (3x+7)(x-1) Factors, Roots and Zeros

Factors, Roots and Zeros

Page 3: 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

Page 4: Warm Up Foil (3x+7)(x-1) Factors, Roots and Zeros

Example

(x - 3) and (x + 5) are Factors of the polynomial

𝐹𝑎𝑐𝑡𝑜𝑟 :𝑥2+2 𝑥−15

Answer: (x-3)(x+5)

22 15x x

Page 5: Warm Up Foil (3x+7)(x-1) Factors, Roots and Zeros

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…

Page 6: Warm Up Foil (3x+7)(x-1) Factors, Roots and Zeros

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

Page 7: Warm Up Foil (3x+7)(x-1) Factors, Roots and Zeros

Example f(x) = x2 - 4

Identifying Solutions4

2

-2

-4

-5 5

Solutions are -2 and 2.

Page 8: Warm Up Foil (3x+7)(x-1) Factors, Roots and Zeros

Now you try this problem.

f(x) = 2x - x2

Solutions are 0 and 2.

Identifying Solutions

4

2

-2

-4

5

Page 9: Warm Up Foil (3x+7)(x-1) Factors, Roots and Zeros

Try this problem y = x2 - 2x - 8.

Roots?Zeros?

Graphing Quadratic Equations

x y-2-1134

4

2

-2

-4

5