Polynomial Division, Equation Solutions, and Factoring Examples
Learn how to divide polynomials, find solutions to equations, factor polynomial functions, and calculate roots in various mathematical problems. Explore in depth step-by-step solutions with illustrative images.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Determine the quotient and the remainder when the first polynomial is divided by the second. 3 2 x - 14x + 51x - 54; x - 9 x + 2 5 ; 6 0 x
Determine the quotient and the remainder when the first polynomial is divided by the second. + + 6 4 3 3 5z - 21z + 20z - 100; z 4 z + z 3 5 25 ; 0 z
Find the other solutions to the equation given. + = 3 2 x 16x - 23x 102 where a is 3 solution = = 17 , 2 x x
Find an equation of least degree for y in terms of x. = + + 3 2 3 2 2 y x x x
What is the degree of the polynomial function given by the table below. degree= 4
Use your calculator to find the zeros of the polynomial function. Use this information to factor the polynomial into linear factors. 9 2 ) ( + = x x x f 4 3 2 18 109 84 x x + + + ) 7 ( 4 )( 3 )( 1 )( 2 x x x x
Factor 2+ 16 b + ( 4 )( 4 ) b i b i
Find all solutions to = 3 2 27 18 12 8 m m m = m 2 3
Factor 4 2 2 3 5 2 a a b b + 2 2 3 ( )( 2 ) a b a b
Factor + 3 2 2 12 5 30 x x x + 2 ( 6 )( 2 ) 5 x x
Factor 7 128 c + + + + 6 5 4 3 2 ( 2 )( 2 4 8 16 32 64 ) c c c c c c c
Factor n 3 3 125 27 m + + 2 2 5 ( 3 )( 25 15 9 ) n m n mn m
Factor 6 512 x + + 2 4 2 ( 8 )( 8 64 ) x x x
Find the four fourth roots of 64. 2 , 2 2 , 2 2 2 , 2 2 i i
Find all the solutions to 2 + i x + = 4 3 2 2 10 25 0 x x given that one solution is = 2 + x i
Factor over the set of polynomials with complex coefficients. 2 + c c + 2 2 + + + ( 1 )( 1 ) c i c i
What are the three linear factors of f(x)? Find a polynomial of degree three which is a factor of f(x)? + + ) 3 6 ( 2 ), 3 ( 1 ), ( x x x x 7 x
Let z = 7 + 6i and w be the complex conjugate of z. Express z - w in a + bi form. 12 i
Let z = 7 + 6i and w be the complex conjugate of z. Express in a + bi form w z 13+ i 84 85 85
True or False. The equation p(x) = x8 - 1 has eight complex zeros. True, Number by of Polynomial a of Zeros Theorem
True or False. Every polynomial function with real coefficients that has a zero 3+2i also has a zero 3-2i. True, Conjugate by Zeros Theorem
True or False. It is possible for the graph of a third-degree polynomial with real coefficients to cross the line y = 4 exactly twice. False, p(x) 4 - = a is 0 polynomial with coefficien real ts. By the Conjugate Zeros Theorem, it has an even number of nonreal zeros.
