What is the polynomial remainder theorem?

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Examples

Lessons

Understanding the remainder Theorem
Prove the Remainder Theorem
Finding the Remainder Using Synthetic Division and the Remainder Theorem
Find the remainder when $\left( {4{x^3} - 7x + 10} \right)$ $(4 x^{3} - 7 x + 10)$ is divided by $\left( {2x - 5} \right)$ $(2 x - 5)$
1. Using synthetic division
2. Using the remainder theorem
When $\left( {8{x^3} + a{x^2} + bx - 1} \right)$ $(8 x^{3} + a x^{2} + b x - 1)$ is divided by:
i) $\left( {2x - 5} \right)$ $(2 x - 5)$ , the remainder is $54$ $54$
ii) $\left( {x + 1} \right)$ $(x + 1)$ , the remainder is $- 30$ $- 30$
Find the values of $a$ $a$ and $b$ $b$ .

Topic Notes

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.

\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})

Remainder theorem

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Remainder theorem

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