Remainder Theorem and Synthetic Division of Polynomials

This precalculus video tutorial provides a basic introduction into the remainder theorem and how to apply it using the synthetic division of polynomials. It explains how to evaluate a function using synthetic division. The value of the function is equal to the remainder when f(x) is divided by a linear factor. This video contains plenty of examples and practice problems on the remainder theorem and synthetic division.
Introduction to Polynomials:
• Polynomials - Classify...
Polynomials - Basic Operations:
• Polynomials - Adding, ...
Dividing Polynomials By Monomials:
• Dividing Polynomials B...
How To Graph Polynomial Functions:
• How To Graph Polynomia...
Intermediate Value Theorem:
• Intermediate Value The...
_____________________________________
Long Division - Polynomials:
• Long Division With Pol...
Polynomial Long Division - More Examples:
• Polynomials - Long Di...
Synthetic Division of Polynomials:
• Synthetic Division of ...
Remainder Theorem & Synthetic Division:
• Remainder Theorem and ...
Factor Theorem & Synthetic Division:
• Factor Theorem and Syn...
Rational Zero Theorem:
• Finding All Zeros of a...
______________________________________
Real & Imaginary Solutions - Polynomials:
• How To Find The Real &...
Solving Polynomial Equations - Synthetic D:
• Solving Polynomial Equ...
Solving Polynomial Equations With Excel:
• Solving Polynomial Equ...
Writing Polynomial Functions Given Zeros:
• Writing Polynomial Fun...
Descartes Rule of Signs:
• Descartes Rule of Signs
Solving Polynomial Inequalities:
• Solving Polynomial Ine...
_____________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/
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I'm just advance studying since I'm being grade 10 next school year, and it was said that this was one of their lessons. I tried to make fun of the equations and made my own equations and still, f(c) and tbe remainder is ALWAYS the same, which I was so amazed how accurate this theorem is. Thanks!

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How does he take 0 as a coefficient of X?

[@krislegends]

@@jbwoy5615 because all terms of an equation has a power, from lowest to highest. Then if one term is missing, then the variable of that power must have a coefficient of 0, which when multiplied by zero equals zero. In math, anything equal to zero is not included.

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Wait the original expression had, - 12, not 12

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@@raid2654 he meant the original expression. it was positive 12.

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hi idk if u can see this but at 8:33 they added two zeros and I'm lost can u please explain why they added the two zeros even though it had x^2/xsquired since they explained at 5:15 we add zero because it doesn't have x^2/xsquired

[@ssinistershorts]

@@blep295 heyy idk if you still need help but imma help you,
alright so the equation has 2x^4 and then 3x^2 then 30 which has no x, in such situations you have to add numbers to replace the missing power, in this case it a number with a power of 3 and a power of 1. when u add the non existing powers you always have to add them as 0x^n where 0 is constant and n is the power missing. if the equation had a number with the power of 5 but no number with the power of 4 then you will have to add 0x^4.
so the equation in the end (the one in the video) would look like:
2x^4 + 0x^3 - 3x^2 - 0x + 30
(notice that you dont write the number 1 when the number is to the power of 1)
hope this explained c: if you still need help you can reply and ill be sure to help you.

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On the second question why did they add zero

[@lexipalmieri7358]

@@user-yy3xd4vl8s because the exponents need to go in descending order for synthetic (and long division w/ polynomials) to work. I can’t remember example 2, but another example would be 3x^4 - 2x^2 + 4x - 5. There is no x^3 in that polynomial, but technically there is a 0x^3 (since zero times anything is zero, it doesn’t change its value) so you would just put a 0 in between the 3 and -2 (in this random example I made up) when dividing. Hope this helped

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