Remainder theorem

Lesson: 1
6:32
Lesson: 2a
3:02
Lesson: 2b
2:04
Lesson: 3
9:18

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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.

Basic Concepts: Polynomial long division, Polynomial synthetic division

Lessons

\cdot

When a polynomial,

P(x)

, is divided by

(x-a)

: Remainder

=P(a)

\cdot

When a polynomial,

P(x)

, is divided by

(ax-b)

: Remainder

=P(\frac{b}{a})

1.
Understanding the remainder Theorem
Prove the Remainder Theorem

2.
Finding the Remainder Using Synthetic Division and the Remainder Theorem
Find the remainder when $\left( {4{x^3} - 7x + 10} \right)$ is divided by $\left( {2x - 5} \right)$
a)
Using synthetic division

b)
Using the remainder theorem

3.
When $\left( {8{x^3} + a{x^2} + bx - 1} \right)$ is divided by:
i) $\left( {2x - 5} \right)$ , the remainder is $54$
ii) $\left( {x + 1} \right)$ , the remainder is $- 30$
Find the values of $a$ and $b$ .

Remainder theorem

Remainder theorem

Lessons

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