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Vocabulary
Adding Polynomials
Subtracting Polynomials
Multiplying Polynomials
Rules
100
How many terms are in a trinomial?
Three
100
(x+5)+(3x+9)
4x + 14
100
(7x+4)-(5x+8)
2x-4
100
(3x+1)(2x+3)
6x2+12x+3
100

Any base raised to the power of zero is equal to one.

Zero Power rule

200
What is the DEGREE of 2x4+9x3-5x2+6
4
200
(3x2+4x)+(2x2-3x)
5x2+x
200
(6x2+4)-(3x2+5)
3x2-1
200
(2x-5)(3x+2)
6x2-4x-10
200

Multiply powers together when raising a power by another exponent, (a^m)^n = a^mn

Power of a Power

300
How many terms are in this polynomial? 4y5+6xy-3x2
Three
300
(-4x2+2x-3)+(5x2-4x+8)
x2-2x+5
300
(2x-4)-2(4x-2)
-6x
300
(2x-4)(3x2-6x+1)
6x3-24x2+26x-4
300

When dividing two bases of the same value, you subtract the exponent values.

Example:

5^5 รท  5^3 = 5^2

Quotient of Powers

400

Write an example of a polynomial with 4 terms and degree of 3.

Show your responses on the white boards!

400
(8x2-4x+3)+(7x2+2x-11)
15x2-2x-8
400
(6x2-5x+8)-(4x2-7x+9)
2x2+2x-1
400
(2x2-4x+6)(x2+5x-2)
2x4+6x3-18x2+38x-12
400

When any base is being multiplied by an exponent, you distribute the exponent to each part of the base.

(๐’™^2๐‘ฆ^2)^3  = x^6y^6

Power of a product

500
Like terms need to have...(two things!!)
1. Same variables 2. Same exponents
500
(5x3+4x2-2x+2)+2(2x3-2x2+x+5)
9x3+12
500
(6x3+4x2-4x+5)-2(2x3-3x2+5x-5)
2x3+10x2-14x+15
500
Ms. Waters wants to know how many desks can fit in her classroom next year. The length of her classroom is x+5 ft and the width of her classroom is x-4 ft. What is the area of her classroom? Area = lw
x2+x-20 square ft
500

Add powers together when multiplying like bases, a^m ร— a^n = a^m+n

Product of Powers