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Polynomial Monomial or the sum of monomials
Degree of the term
The exponent of the variable
Standard form of a polynomial
The terms of the polynomial are written in descending order by the degree of the term.
Degree of the polynomial
The largest degree of any term of the polynomial.
Classify using the degree of the polynomial(First Name)
Degree Name using Degree0 Constant1 Linear2 Quadratic3 Cubic4 Quartic5 Quintic
Classify using the number of terms(Last Name)
Number of Term
Name using the number of terms
1 Monomial2 Binomial3 trinomial4 OR MORE Polynomial
Example #1: Classify the polynomial. Then write in standard form
Examples of Polynomials
Classify the polynomial
Standard form
63 + x3x2
3x2+ x4
-2x + 2x3+ 5x2
-x + 2x – 3x2 – 2x5+ 4
You Try….
Classify & Write the polynomial in standard form.
1) -7x + 5x4
2) x2- 4x + 3x2+ 2x
Adding & Subtracting Polynomials…You can only add & subtract like terms (CLT)
Example #2: Add or Subtract
Examples: Multiply1) Multiply. Then classify the polynomial.
2) Multiply. Then classify the polynomial.
3) Multiply. Then classify the polynomial.
4) Multiply. Then classify the polynomial.
You Try….Multiply. Then classify the polynomial.
Don’t forget about area formulas for the other shapes…
Examples: Area & Perimeter.
Examples: Volume1)Find the volume of the rectangular prism.
Multiply (x + 1)8……
Yes, there is a short cut: The Binomial Theorem.
Before we understand the pattern, let’s talk about Pascal’s Triangle.
Pascal’s Triangle is a triangular array of numbers formed by first lining the border with 1’s and then placing the sum of the two adjacent numbers within a row between and underneath the 2 original numbers.
Expand (Multiply) (a + b)4
1st: Number the terms
2nd: Use the pattern to simplify the each term
3rd: Simplify
Examples: Expand
1) (x + 2)3
2) (x – 4)4
3) (v + w)9
4) (2x – 3)5
You try…
1) (x – 1)4 2) (g + h)6 3) (c – 2)5
Section 2.5 Function OperationsA function is a relation in which each element of the domain (x-values) is paired with exactly one element in the range (y-values).
Visuals help….Wet clothes → Dryer → Dry Clothes
Input → equation → output
x → f(x)→ y
Recall…If f(x) = x + 5, thenx f(x)
Example #1: Adding, Subtracting & Multiplying FunctionsLet f(x) = 3x + 8, g(x) = 2x -12 and h(x) = -4x
1) f + g =
2) f – g =
3) g – f =
4) g * f =
5) g * h =
6) h – f =
Composite functions
In other words…
f(x) → g(x) →(g ○ f)
Example #2: Composition of a FunctionLet f(x) = x – 2 and g(x) = x2.
1) f(f(-5))
2) g(f(0))
3) f(g(-2))
4) f(g(3))
You try… Let f(x) = 3x + 5 and g(x) = x2
1) f(x) + g(x)
2) f(x) * g(x)
3) f(g(x))
Section 2.6 Inverse Functions
In other words, the input and output switches places…
Example #1: Find the inverse from a table of points.
Example #2: Find the inverse from an equation.
Step 1: Switch x & yStep 2: solve for y.
1) y = x2 + 3
2) y = √ x+1
3) y = 2x + 6