- Home
- AS-Level Maths
- Algebraic Division
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.