Determine the Formula of Factor Theorem – Essay – Elaiza Herrera
Search
Essays
Sign up
Sign in
Contact us
Tweet
Index
/English
Determine the Formula of Factor Theorem
Module InMath(Factor Theorem)Submitted By: Jean Anne Marie C. Romulo G10- Aguinaldo Submitted To: Sir Nick Hermoso Factor TheoremObjectivesDetermine the formula of Factor TheoremAble to explain what Factor Theorem is and use this to solve a problem.TopicIn algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial [pic 1] has a factor [pic 2] if and only if [pic 3] (i.e. [pic 4] is a root).The point of the Factor Theorem is the reverse of the Remainder Theorem: If you synthetic-divide a polynomial by x = a and get a zero remainder, then, not only is x = a a zero of the polynomial (courtesy of the Remainder Theorem), but x – a is also a factor of the polynomial (courtesy of the Factor Theorem).It is commonly applied to factorizing and finding the roots of polynomial equations. The theorem states that [pic 5] is a factor of a polynomial f(x)if [pic 6];that is, r is a root off(x). Factor theorem problems are typically solved by applying synthetic division and then checking for a zero remainder. The remainder theorem is often used with the factor theorem. It states that if a polynomial f(x) is divided by a linear divisor [pic 7], the remainder is f(r). If [pic 8], then the remainder is 0 and [pic 9], showing that [pic 10] is a factor of f(x).
5 Solving ProblemShow that y+4 is a factor of g(y) = 5y4+16y3−15y2+8y+16 g(y) = 5y4+16y3-15y2+8y+16 g(-4) = 5(-4)4+16(-4)3+ 15 (-4)2 + 8(-4) +16 = 5(256) + 16 (-64) + 15(16) + 8(-4) +16 = 1280 – 1024 – 240 – 32 + 16 = 0Determine whether x-2 is a factor of x2 – 7x + 10=x2 -7x +10=22 – 72 + 10= 4 – 14 + 10= 0 Determine whether x-3 is the factor of x3 – 3×2 + 4x -12= (3)3 – 3(3)2 + 4(3) – 12= 27 – 27 + 12 -12= 0 Show that x+1 is a factor of 2×3 + 5x – 9x -12 = 2(-1)3 + 5(-1) – 9(-1) – 12 = -2 + 5 + 9 -12 = 0Show that x + 1 is a factor of 2x – 2×2 – 2x +12= 2(1) – 2(1)2 – 2(1) + 12 = 2 – 2 – 2 + 2= 010 Exercise Show that (x+4) is a factor of 4x + 8×2 – 6x + – 7Show that (x+1) is the factor of 3x +8x -5x +1 Show that (x-1) is the factor of 3×3 – 8×2 + 3x + 2Show that (x-2) is the factor of x3 – 7x + 5Show that (x-2) is the factor of 4×4 – 3×3 –x2 + 2x + 1Show that (x-2) is the factor of 7×2 + 4×3 –x2 + 2x +1Show that (x+3) is the factor of 4×2 – 2×2 – x 2 – 2x +1 Show that (x+3) is the factor of 2×2 – 3×2 –x2+2x + 1Show that (x-4) is the factor of 2×2 – 5x – 12 Show that (x-5) is the factor of x3 -25x -5V. References
Continue for 4 more pages »
Read full document
Download as (for upgraded members)
Citation Generator
MLA 7
CHICAGO
(2017, 09). Determine the Formula of Factor Theorem. EssaysForStudent.com. Retrieved 09, 2017, from
“Determine the Formula of Factor Theorem” EssaysForStudent.com. 09 2017. 2017. 09 2017 <
"Determine the Formula of Factor Theorem." EssaysForStudent.com. EssaysForStudent.com, 09 2017. Web. 09 2017. <
"Determine the Formula of Factor Theorem." EssaysForStudent.com. 09, 2017. Accessed 09, 2017.
Essay Preview
By: Elaiza Herrera
Submitted: September 1, 2017
Essay Length: 1,106 Words / 5 Pages
Paper type: Essay Views: 341
Report this essay
Tweet
Related Essays
Factors Determining Premium Income Of
Contents Chapter – 01 3 1.00: Introduction and Problem Statement 3 Chapter-02 4 2.00: Review of Literature 4 Chapter - 03 6 3.00: Development of
2,766 Words | 12 Pages
George Washington, Determining Factor of Us over British
George Washington: The Determining Factor for the American’s Win Over the British George Washington, in my mind, was the largest determining factor in the American’s
1,574 Words | 7 Pages
Factors That Determine the Currency Exchange Rates
Factors that Determine the Currency Exchange Rates Exchange rate is often referred to as the nominal exchange rate. It is defined as the rate at
1,709 Words | 7 Pages
What I Tell You Three Times Is True (lewis Carroll) Might This Formula or a More Sophisticated Version of It - Actually Determine What We Believe to Be True?
Repetition is our way of learning knowledge. Repetition is drilling something to memory, reinforcing the idea in our heads. It is the key to reflexive
1,250 Words | 5 Pages
Similar Topics
What economic and social factors should Fresh Fields managers watch
FreeWill Determinism Problem Greek Philosophy
Get Access to 89,000+ Essays and Term Papers
Join 209,000+ Other Students
High Quality Essays and Documents
Sign up
© 2008–2020 EssaysForStudent.comFree Essays, Book Reports, Term Papers and Research Papers
Essays
Sign up
Sign in
Contact us
Site Map
Privacy Policy
Terms of Service
Facebook
Twitter