ALG-09

Remainder theorem

P(r) is the remainder of P(x) divided by (x − r). Quadratic snapshot.

Reading speed

PolynomialsRemainder theorem

Governing equation

P(r)=ar^2+br+c

where

a: a (—)
b: b (—)
c: c (—)
r: r (—)
P(r): Remainder (—)

Lecture brief

Historical brief

From al-Khwārizmī’s restoration to the quadratic formula, AM–GM, De Moivre and logarithms, algebra is the closed-form skeleton under every lab. These sheets solve, bound and compound. This sheet (ALG-09 — Remainder theorem) is the form associated with Remainder theorem. Working symbols: $a$ , $b$ , $c$ , $r$ $\rightarrow$ $P(r)$ . Write P(x) = (x−r) Q(x) + R. Setting x = r gives R = P(r).

Purpose

Purpose: compute

P(r)

from

a

b

c

r

in Algebra via

P(r)=ar^2+br+c

P(r) is the remainder of P(x) divided by (x − r). Quadratic snapshot. Use it when a real algebra question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

a = 1.000\,\mathrm{—}

b = -2.000\,\mathrm{—}

c = -3.000\,\mathrm{—}

r = 2.000\,\mathrm{—}

, the governing relation

P(r)=ar^2+br+c

yields

P(r) = -3.0000\,\mathrm{—}

. P(x) = ax² + bx + c, evaluate at r. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

a a1 —b b-2 —c c-3 —r r2 —

Outputs

Remainder P(r)-3.0000 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

P(x) = ax² + bx + c, evaluate at r.

Write P(x) = (x−r) Q(x) + R. Setting x = r gives R = P(r).

Reading speed

Watch on YouTube