Unit 2 - Operations with polynomials
This unit develops the structural similarities between the system of polynomials and the system of integers. Students draw on analogies between polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property. Students connect multiplication of polynomials with multiplication of multi-digit integers, and division of polynomials with long division of integers. Students will find inverse functions and verify by composition that one function is the inverse of another function
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Rewrite rational expressions
MGSE9-12.A.APR.1 Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.
MGSE9-12.A.APR.5 Know and apply that the Binomial Theorem gives the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle
MGSE9-12.A.APR.6 Rewrite simple rational expressions in different forms using inspection, long division, or a computer algebra system; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x).Perform arithmetic operations on polynomials
MGSE9-12.A.APR.5 Know and apply that the Binomial Theorem gives the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle
MGSE9-12.A.APR.6 Rewrite simple rational expressions in different forms using inspection, long division, or a computer algebra system; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x).Perform arithmetic operations on polynomials
Sub work: You choose either p 16&17 which is simplifying radicals OR p 34 which is completing the square problems.
Look at 2 animated examples
* polynomials
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Try these 10 addition and subtraction polynomial practice with edia!
Try 1-10 or up 20
* polynomials practice with answers
Try your skills at adding, subtracting, and multiplying polynomials
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Long division polynomial/trinomial
Try these polynomial long division problems & check your answers.
6 practice long division problems with answers
How the coefficients work
Explanation of the binomial expansion
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Long division trinomial/binomial
Edia long division polynomial practice with feedback
Synthetic division with polynomials
6 practice synthetic division problems with answers
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Multiply multivariable polynomials
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The secrets of Pascal's triangle
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Who is Pascal
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Monomial ONLY divided into a polynomial
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Long division & synthetic division of polynomials
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Practice 10 polynomial division
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Build a function that models a relationship between two quantities
MGSE9-12.F.BF.1 Write a function that describes a relationship between two quantities. MGSE9-12.F.BF.1b Combine standard function types using arithmetic operations in contextual situations (Adding, subtracting, and multiplying functions of different types).
MGSE9-12.F.BF.1c Compose functions.
MGSE9-12.F.BF.1 Write a function that describes a relationship between two quantities. MGSE9-12.F.BF.1b Combine standard function types using arithmetic operations in contextual situations (Adding, subtracting, and multiplying functions of different types).
MGSE9-12.F.BF.1c Compose functions.
How to evaluate functions
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Story of a function
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IXL evaluating function practice
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Function composition quiz
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Edia - Functions Practice…all about function operations!
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Explanation of composition of functions
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Build new functions from existing functions
MGSE9-12.F.BF.4 Find inverse functions. MGSE9-12.F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2(x3 ) or f(x) = (x+1)/(x-1) for x ≠ 1. MGSE9-12.F.BF.4b Verify by composition that one function is the inverse of another. MGSE9-12.F.BF.4c Read values of an inverse function from a graph or a table, given that the function has an inverse.
MGSE9-12.F.BF.4 Find inverse functions. MGSE9-12.F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2(x3 ) or f(x) = (x+1)/(x-1) for x ≠ 1. MGSE9-12.F.BF.4b Verify by composition that one function is the inverse of another. MGSE9-12.F.BF.4c Read values of an inverse function from a graph or a table, given that the function has an inverse.
How to find the inverse of a function
These functions are inverses of each other
Verify if functions are inverses
Practice with inverse functions
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Inverse practice with answers
These functions are not inverses of each other
Composition of function notation & example
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