Polynomial Division (AQA A-Level Mathematics): Flashcards

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Polynomial Division
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What does a polynomial contain?

Positive integer powers of xx and constants

First step in polynomial division

Divide leading terms

Remainder Theorem application

Substitute x=ax=a into f(x)f(x) to find remainder

Factor Theorem condition

(xa)(x-a) is factor when f(a)=0f(a)=0

Quotient in 72\frac{7}{2}

33

Remainder in 72\frac{7}{2}

11

Year 1 vs Year 2 polynomial division

Year 1: linear divisor; Year 2: linear or higher degree

General form after dividing P(x)D(x)\frac{P(x)}{D(x)}

Q(x)+R(x)D(x)Q(x) + \frac{R(x)}{D(x)}

Quotient of x2+3x+5x+1\frac{x^2+3x+5}{x+1}

x+2x+2

Remainder of x2+3x+5x+1\frac{x^2+3x+5}{x+1}

33

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