Answer:(ax+b) (x+a)
Use FOIL on second term
Assignment details:
It's time to show off your creativity and marketing skills!
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. See what happens when different binomials or trinomials are combined. Below is a list of some sample factors you may use to help develop your own identity.
• (x – y)
• (x + y)
• (y + x)
• (y – x)
• (x + a)
• (y + b)
• (x2 + 2xy + y2)
• (x2 – 2xy + y2)
• (ax + b)
• (cy + d)
The numerical proof is correct! This identity had been proven right in front of your eyes
Algebraic Proof
Amber Carter
Polynomial Identities
So, you want even more proof? Well then lets just substitute in values for a, b, and x. Lets make a=2, b=4, and x=6.
(ax+b) (x+a) = ax^2 +a^2x +bx +ab
(ax+b) (x+a)
+bx +ab
(ax+b) (x+a)=ax^2 +a^2x +bx +ab
This identity is effective and easy to use!
The New Identity
To solve this you have to use the distributive property, more specifically FOIL
Use FOIL on first term
ax^2+a^2x+bx+ab
((2*6)+4) (6+2) = (2^2*6) +(4^2*6) +(2*4)
128 = 128
(16) (8) = (24)+(96)+(8)
Module 4.08
Numerical Proof
I hope this was adequate proof to convince you to love my new polynomial proof!
ax^2+a^2x
The following is an advertisement for the newest polynomial identity. If you like the way your life is now and do not wish to add this new identity to your knowledge, then please do not go any further. This identity is not for those who are non-accepting of new and improved ideas.
Step-by-step explanation:
![\bf \qquad \qquad \textit{Future Value of an ordinary annuity}\\ \left. \qquad \qquad \right.(\textit{payments at the end of the period}) \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7BFuture%20Value%20of%20an%20ordinary%20annuity%7D%5C%5C%0A%5Cleft.%20%5Cqquad%20%5Cqquad%20%5Cright.%28%5Ctextit%7Bpayments%20at%20the%20end%20of%20the%20period%7D%29%0A%5C%5C%5C%5C%0AA%3Dpymnt%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7Br%7D%7Bn%7D%20%5Cright%29%5E%7Bnt%7D-1%7D%7B%5Cfrac%7Br%7D%7Bn%7D%7D%20%5Cright%5D)
![\bf A=1200\left[ \cfrac{\left( 1+\frac{0.05}{1} \right)^{1\cdot 12}-1}{\frac{0.05}{1}} \right]\implies A\approx 19100.55](https://tex.z-dn.net/?f=%5Cbf%20A%3D1200%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7B0.05%7D%7B1%7D%20%5Cright%29%5E%7B1%5Ccdot%20%2012%7D-1%7D%7B%5Cfrac%7B0.05%7D%7B1%7D%7D%20%5Cright%5D%5Cimplies%20A%5Capprox%2019100.55)
