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# 4.08 Polynomial Identities and Proofs

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## Quiyara Murphy

on 24 July 2016

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#### Transcript of 4.08 Polynomial Identities and Proofs

LET'S LOOK
STEP ONE
Create your own identity by squaring one factor from column A and adding it to one factor from column B.
STEP TWO
Check polynomial identity
STEP THREE
Plug in the values for a , b , and x.
IDENTITY:
FOUND
:)
You are going to design an advertisement for a new polynomial identity that you are going to invent. Your goal for this activity is to demonstrate the proof of your polynomial identity through an algebraic proof and a numerical proof in an engaging way! Make it so the whole world wants to purchase your polynomial identity and can't imagine living without it!

You may do this by making a flier, a newspaper or magazine advertisement, making an infomercial video or audio recording, or designing a visual presentation for investors through a flowchart or PowerPoint.

You must:

Label and display your new polynomial identity
Prove that it is true through an algebraic proof, identifying each step
Demonstrate that your polynomial identity works on numerical relationships
Warning! No identities used in the lesson may be submitted. Create your own using the columns below. See what happens when different binomials or trinomials are combined. Square one factor from column A and add it to one factor from column B to develop your own identity.
4.08 Polynomial Identities and Proofs
Quiyara Murphy
Column A Column B
(x − y) (x2 + 2xy + y2)
(x + y) (x2 − 2xy + y2)
(y + x) (ax + b)
(y − x) (cy + d)
(ax + b)(x +a) = (ax^2 + a^2(x) + bx +ab)
FOIL
ax^2 + a^2 (x) + bx +ab
(ax + b) (x + a)
a = 3
b = 6
x = 2
(ax + b) (x + a) = ax^2 + a^2(x) + bx + ab
(3 (2) + 6) (3 + 2) = 3 (4) + 9 (2) + 6 (2) + 3 (6)
(12) (5) = (12 + 18 + 12 + 18)

60 = 60
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