Polynomial Functions

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by mdrogt
Last updated 4 years ago

Discipline:
Math
Subject:
Number Operations
Grade:
11

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Polynomial Functions

Polynomial Functions

How to Graph Polynomial Functions and Describe End BehaviorEnding behavior- Direction of the graph to the far left and to the far rightLeading Coefficent Positive: Even Degree: Up and upOdd Degree: Down and up Leading Coefficent Negative: Even Degree: Down and downOdd Degree: Up and down Example:y=4x^3 -3xDown and up;4 is a positive coefficent -3 is negative

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How To Write A Polynomial Function From Its Zeros In Standard Form Example:Write a polynomial in standard form with zeros at 2, -3, and 0.Write a linear factor for each zero:y= (x-2)(x+3)(x-0)Simplify (x-0) =x(x-2)(x+3)Multiply (x-2)(x+3)= x(x^2 + x-6)Distribute x through= x^3 + x^2 -6xAnswery= x^3 + x^2 -6x

How to Identify Relative Maximums and Minimums Relative maximum- The greatest y-value of the points in a region of graphRelative minimum- The least y-value among nearby points on a graphExample:What are the relative maximum and minimum of f(x)= -4x^3 + 12x^2 + 4x -12Type the equation into your graphing calculator. Go to the menu, and press analyze graph. From there, press the minimum button. Drag the boundaries on the left to the right of the lowest part of the graph. That is your minimum. Do the same for your maximum, only on the highest point of the graph. Maximum: 2.155, 12.317Minimum: -0.155, -12.317

How To Factor Polynomial Expressions To factor polynomial expressions, you can:Factor by grouping (4 terms) ax+ay+bx+by= a(x+y) + b(x+y) = (a+b)(x+y)ExampleFactor x^3 +2x^2 - 3x-6x^2(x+2) -3(x+2)(x+2)(x^2-3)Sum of Cubes a^3+b^3= (a+b)(a^2-ab+b^2)ExampleFactor x^3-8cubed root of x^3=xcubed root of 8= 2(x-2)(x^2+2x+4) Difference of Cubesa^3-b^3=(a-b)(a^2+ab+b^2)ExampleFactor x^3+27cubed root of x^3 is xcubed root of 27 is 3(x+3)(x^2-3x+9)

How to Divide Polynomials Using Long Division 1. Put each polynomial in standard form with zero coefficents where appropriate.2. Divide, multiply, subtract, and repeat until the degree of the remainder is less than the divisor.

How to Divide Polynomials Using Synthetic Division 1. Write coefficents (including zeros) of the polynomial in standard form. For the divisor, use the value for x such that x-a+0. (use a)2.Bring down the first coefficent 3. Multiply the divisor and add it to the next coefficent. 4. Continue through to the last coefficent.

Special cases of factored polynomials

How to classify and name polynomialDegree Terms1 linear 1 monomial2 quadratic 2 binomial 3 cubic 3 trinomial4 quartic 4 polynomial5 quintic

How to solve polynomial equations by factoring

How to analyze the factored form of a polynomial

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