- Home
- Math 30-2 (Alberta)
- Polynomial Functions
Remainder theorem
- Lesson: 16:32
- Lesson: 2a3:02
- Lesson: 2b2:04
- Lesson: 39:18
Remainder theorem
You may want to refresh your memory on polynomial long division and synthetic division to better understand this lesson. The remainder theorem simply states that if a polynomial f(x) is divided by a linear expression x-r, the value of f(r) is equal to the remainder.
Related Concepts: Integration of rational functions by partial fractions
Lessons
⋅ When a polynomial, P(x), is divided by (x−a): Remainder =P(a)
⋅ When a polynomial, P(x), is divided by (ax−b): Remainder =P(ab)
⋅ When a polynomial, P(x), is divided by (ax−b): Remainder =P(ab)
- 1.Understanding the remainder Theorem
Prove the Remainder Theorem
- 2.Finding the Remainder Using Synthetic Division and the Remainder Theorem
Find the remainder when (4x3−7x+10) is divided by (2x−5)a)Using synthetic divisionb)Using the remainder theorem - 3.When (8x3+ax2+bx−1) is divided by:
i) (2x−5), the remainder is 54
ii) (x+1), the remainder is −30
Find the values of a and b.
Do better in math today
3.
Polynomial Functions
3.1
What is a polynomial function?
3.2
Polynomial long division
3.3
Polynomial synthetic division
3.4
Remainder theorem
3.5
Factor theorem
3.6
Rational zero theorem
3.7
Characteristics of polynomial graphs
3.8
Multiplicities of polynomials
3.9
Imaginary zeros of polynomials
3.10
Determining the equation of a polynomial function
3.11
Applications of polynomial functions
3.12
Solving polynomial inequalities
3.13
Fundamental theorem of algebra
3.14
Descartes' rule of signs