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Unit 2A: Polynomials, Part 1
2017
pebblebrook high schoolALGBRA 2
2A.1 – 1B.6
2A.1 Classify PolynomialsVocabulary:
Polynomial
Degree of the term
Standard form of a polynomial
Degree of the polynomial
Classify using the degree of the polynomial(First Name)
Degree Name using Degree0 Constant1 Linear2 Quadratic3 Cubic4 Quadratic5 Quantic
Classify using the number of terms(Last Name)
Number of Term
Name using the number of terms
1 Monomial2 Binomial3 trinomial4 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
You Try…..
Section 2A.1 HomeworkClassify the polynomial and write in standard form.
Simplify the polynomial.
2A.2 Multiplying Polynomials
Method….Use area method (Box)Examples: Multiply
1) 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.
Section 2A.2 Homework
2A.3 Word Problems: Area, Volume, & Perimeter.
Area = lw Volume = lwh Perimeter = add lengthsDon’t forget about area formulas for the other shapes…
Examples: Area & Perimeter.
Examples: Volume
1)Find the volume of the rectangular prism.
2) Find the volume of the rectangular prism.
You try…
Section 2A.3 Homework
Section 2A.4 Binomial Theorem
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: Use Pascal’s Triangle to calculate the coefficients of the 5 terms, where n = 4.
4C0 4C1 4C2
4C3 4C4
2nd: Use the Binomial Theorem to get the exponents of the terms. FIRST DECREASES; SECOND TERM INCREASES.
a4 a3b1 a2b2 ab3 b4
3rd: Make the substitutions and simply if necessary.
a4 + 4a3b1 + 6a2b2 + 4ab3 + b4
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 2A.4 Homework
Section 2A.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)
You can add, subtract, & multiply functions…
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 2A.5 Homework
Section 2A.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
To verify if 2 functions are inverses of one another, you must find the composition of f(g(x)) AND g(f(x)). THE BOTH MUST SIMPLIFY TO X!
Example #3: Verify the functions are inverses of one another.
1)
2)
3)
15. 15.
16.
17.
Section 2A.6 Homework